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15.093 Optimization Methods (SMA 5213) (MIT) 15.093 Optimization Methods (SMA 5213) (MIT)

Description

This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include the simplex method, network flow methods, branch and bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton's method, heuristic methods, and dynamic programming and optimal control methods. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5213 (Optimisation Methods). This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include the simplex method, network flow methods, branch and bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton's method, heuristic methods, and dynamic programming and optimal control methods. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5213 (Optimisation Methods).

Subjects

principal algorithms | principal algorithms | linear | linear | network | network | discrete | discrete | nonlinear | nonlinear | dynamic optimization | dynamic optimization | optimal control | optimal control | methodology and the underlying mathematical structures | methodology and the underlying mathematical structures | simplex method | simplex method | network flow methods | network flow methods | branch and bound and cutting plane methods for discrete optimization | branch and bound and cutting plane methods for discrete optimization | optimality conditions for nonlinear optimization | optimality conditions for nonlinear optimization | interior point methods for convex optimization | interior point methods for convex optimization | Newton's method | Newton's method | heuristic methods | heuristic methods | dynamic programming | dynamic programming | optimal control methods | optimal control methods | SMA 5213 | SMA 5213

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6.832 Underactuated Robotics (MIT) 6.832 Underactuated Robotics (MIT)

Description

Includes audio/video content: AV lectures. Robots today move far too conservatively, using control systems that attempt to maintain full control authority at all times. Humans and animals move much more aggressively by routinely executing motions which involve a loss of instantaneous control authority. Controlling nonlinear systems without complete control authority requires methods that can reason about and exploit the natural dynamics of our machines. This course discusses nonlinear dynamics and control of underactuated mechanical systems, with an emphasis on machine learning methods. Topics include nonlinear dynamics of passive robots (walkers, swimmers, flyers), motion planning, partial feedback linearization, energy-shaping control, analytical optimal control, reinforcement learning/a Includes audio/video content: AV lectures. Robots today move far too conservatively, using control systems that attempt to maintain full control authority at all times. Humans and animals move much more aggressively by routinely executing motions which involve a loss of instantaneous control authority. Controlling nonlinear systems without complete control authority requires methods that can reason about and exploit the natural dynamics of our machines. This course discusses nonlinear dynamics and control of underactuated mechanical systems, with an emphasis on machine learning methods. Topics include nonlinear dynamics of passive robots (walkers, swimmers, flyers), motion planning, partial feedback linearization, energy-shaping control, analytical optimal control, reinforcement learning/a

Subjects

underactuated robotics | underactuated robotics | actuated systems | actuated systems | nonlinear dynamics | nonlinear dynamics | simple pendulum | simple pendulum | optimal control | optimal control | double integrator | double integrator | quadratic regulator | quadratic regulator | Hamilton-Jacobi-Bellman sufficiency | Hamilton-Jacobi-Bellman sufficiency | minimum time control | minimum time control | acrobot | acrobot | cart-pole | cart-pole | partial feedback linearization | partial feedback linearization | energy shaping | energy shaping | policy search | policy search | open-loop optimal control | open-loop optimal control | trajectory stabilization | trajectory stabilization | iterative linear quadratic regulator | iterative linear quadratic regulator | differential dynamic programming | differential dynamic programming | walking models | walking models | rimless wheel | rimless wheel | compass gait | compass gait | kneed compass gait | kneed compass gait | feedback control | feedback control | running models | running models | spring-loaded inverted pendulum | spring-loaded inverted pendulum | Raibert hoppers | Raibert hoppers | motion planning | motion planning | randomized motion planning | randomized motion planning | rapidly-exploring randomized trees | rapidly-exploring randomized trees | probabilistic road maps | probabilistic road maps | feedback motion planning | feedback motion planning | planning with funnels | planning with funnels | linear quadratic regulator | linear quadratic regulator | function approximation | function approximation | state distribution dynamics | state distribution dynamics | state estimation | state estimation | stochastic optimal control | stochastic optimal control | aircraft | aircraft | swimming | swimming | flapping flight | flapping flight | randomized policy gradient | randomized policy gradient | model-free value methods | model-free value methods | temporarl difference learning | temporarl difference learning | Q-learning | Q-learning | actor-critic methods | actor-critic methods

License

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14.471 Public Economics I (MIT) 14.471 Public Economics I (MIT)

Description

This course covers theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy. This course covers theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy.

Subjects

economic analysis | economic analysis | taxation | taxation | wealth | wealth | financial policy | financial policy | income | income | investment | investment | asset | asset | political economy | political economy | labor | labor | capital | capital | public policy | public policy | corporate finance | corporate finance | tax reform | tax reform | optimal commodity taxes | optimal commodity taxes | optimal corrective taxation | optimal corrective taxation | optimal stochastic taxes | optimal stochastic taxes | dynamic consistency issues | dynamic consistency issues | debt | debt | equity | equity

License

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14.471 Public Economics I (MIT) 14.471 Public Economics I (MIT)

Description

Theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy. Theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy.

Subjects

economic analysis | economic analysis | taxation | taxation | wealth | wealth | financial policy | financial policy | income | income | investment | investment | asset | asset | political economy | political economy | labor | labor | capital | capital | public policy | public policy | corporate finance | corporate finance | tax reform | tax reform | optimal commodity taxes | optimal commodity taxes | optimal corrective taxation | optimal corrective taxation | optimal stochastic taxes | optimal stochastic taxes | dynamic consistency issues | dynamic consistency issues | debt | debt | equity | equity

License

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11.487 Urban Public Finance in Developing Countries (MIT) 11.487 Urban Public Finance in Developing Countries (MIT)

Description

This readings-based course analyzes the structure and operation of government systems in developing countries, with particular emphasis on regional and local governments. Major topics include: the role of decentralization in national economic reform programs, the potential impact of decentralized governments on local economic development, determination of optimal arrangements for sharing fiscal responsibilities among levels of government, evaluation of local revenue and expenditure decisions, and assessment of prospects and options for intergovernmental fiscal reform. Emphasis is on basic economic concerns, with consideration given to political, institutional, and cultural factors. This readings-based course analyzes the structure and operation of government systems in developing countries, with particular emphasis on regional and local governments. Major topics include: the role of decentralization in national economic reform programs, the potential impact of decentralized governments on local economic development, determination of optimal arrangements for sharing fiscal responsibilities among levels of government, evaluation of local revenue and expenditure decisions, and assessment of prospects and options for intergovernmental fiscal reform. Emphasis is on basic economic concerns, with consideration given to political, institutional, and cultural factors.

Subjects

basic economic concerns | basic economic concerns | political | political | institutional | institutional | and cultural factors | and cultural factors | decentralization in national economic reform programs | decentralization in national economic reform programs | the potential impact of decentralized governments on local economic development | the potential impact of decentralized governments on local economic development | determination of optimal arrangements for sharing fiscal responsibilities among levels of government | determination of optimal arrangements for sharing fiscal responsibilities among levels of government | evaluation of local revenue and expenditure decisions | evaluation of local revenue and expenditure decisions | assessment of prospects and options for intergovernmental fiscal reform | assessment of prospects and options for intergovernmental fiscal reform | political | institutional | and cultural factors | political | institutional | and cultural factors | developing countries | developing countries | public goods | public goods | externalities | externalities | economic development | economic development | balance sheets | balance sheets | fiscal gap | fiscal gap | revenues | revenues | expenditures | expenditures | budget deficits | budget deficits | inflation | inflation | public finance theory | public finance theory | efficiency | efficiency | optimal taxation | optimal taxation | optimal user fees | optimal user fees | basic microeconomic theory | basic microeconomic theory | equity | equity | incidence | incidence | general equilibrium model | general equilibrium model | property taxation | property taxation | tax reform | tax reform | intergovernmental fiscal relations | intergovernmental fiscal relations | fiscal federalism | fiscal federalism | decentralization | decentralization | transfers | transfers | international lending agencies | international lending agencies | programming assistance | programming assistance | conditionalities | conditionalities | public debt | public debt | structural adjustment | structural adjustment | private sector participation | private sector participation | microfinance | microfinance

License

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1.561 Motion Based Design (MIT) 1.561 Motion Based Design (MIT)

Description

This course presents a rational basis for the preliminary design of motion-sensitive structures. Topics covered include: analytical and numerical techniques for establishing the optimal stiffness distribution, the role of damping in controlling motion, tuned mass dampers, base isolation systems, and active structural control. Examples illustrating the application of the motion-based design paradigm to building structures subjected to seismic excitation are discussed. This course presents a rational basis for the preliminary design of motion-sensitive structures. Topics covered include: analytical and numerical techniques for establishing the optimal stiffness distribution, the role of damping in controlling motion, tuned mass dampers, base isolation systems, and active structural control. Examples illustrating the application of the motion-based design paradigm to building structures subjected to seismic excitation are discussed.

Subjects

preliminary design | preliminary design | motion-sensitive structures | motion-sensitive structures | analytical techniques | analytical techniques | numerical techniques | numerical techniques | optimal stiffness distribution | optimal stiffness distribution | damping | damping | controlling motion | controlling motion | tuned mass dampers | tuned mass dampers | base isolation systems | base isolation systems | active structural control | active structural control | building structures | building structures | wind excitation | wind excitation | seismic excitation | seismic excitation | building design | building design | numerical analysis | numerical analysis | motion control | motion control | motion-based design | motion-based design | safety | safety | serviceability | serviceability | loadings | loadings | optimal stiffness | optimal stiffness | optimal damping | optimal damping | base isolation | base isolation

License

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11.487 Urban Public Finance in Developing Countries (MIT) 11.487 Urban Public Finance in Developing Countries (MIT)

Description

This readings-based course analyzes the structure and operation of government systems in developing countries, with particular emphasis on regional and local governments. Major topics include: the role of decentralization in national economic reform programs; the potential impact of decentralized governments on local economic development; determination of optimal arrangements for sharing fiscal responsibilities among levels of government; evaluation of local revenue and expenditure decisions; and assessment of prospects and options for intergovernmental fiscal reform. Emphasis is on basic economic concerns, with consideration given to political, institutional, and cultural factors. This readings-based course analyzes the structure and operation of government systems in developing countries, with particular emphasis on regional and local governments. Major topics include: the role of decentralization in national economic reform programs; the potential impact of decentralized governments on local economic development; determination of optimal arrangements for sharing fiscal responsibilities among levels of government; evaluation of local revenue and expenditure decisions; and assessment of prospects and options for intergovernmental fiscal reform. Emphasis is on basic economic concerns, with consideration given to political, institutional, and cultural factors.

Subjects

basic economic concerns | basic economic concerns | political | political | institutional | institutional | and cultural factors | and cultural factors | decentralization in national economic reform programs | decentralization in national economic reform programs | the potential impact of decentralized governments on local economic development | the potential impact of decentralized governments on local economic development | determination of optimal arrangements for sharing fiscal responsibilities among levels of government | determination of optimal arrangements for sharing fiscal responsibilities among levels of government | evaluation of local revenue and expenditure decisions | evaluation of local revenue and expenditure decisions | assessment of prospects and options for intergovernmental fiscal reform | assessment of prospects and options for intergovernmental fiscal reform | political | institutional | and cultural factors | political | institutional | and cultural factors | developing countries | developing countries | public goods | public goods | externalities | externalities | economic development | economic development | balance sheets | balance sheets | fiscal gap | fiscal gap | revenues | revenues | expenditures | expenditures | budget deficits | budget deficits | inflation | inflation | public finance theory | public finance theory | efficiency | efficiency | optimal taxation | optimal taxation | optimal user fees | optimal user fees | basic microeconomic theory | basic microeconomic theory | equity | equity | incidence | incidence | general equilibrium model | general equilibrium model | property taxation | property taxation | tax reform | tax reform | intergovernmental fiscal relations | intergovernmental fiscal relations | fiscal federalism | fiscal federalism | decentralization | decentralization | transfers | transfers | international lending agencies | international lending agencies | programming assistance | programming assistance | conditionalities | conditionalities | public debt | public debt | structural adjustment | structural adjustment | private sector participation | private sector participation | microfinance | microfinance

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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14.451 Dynamic Optimization Methods with Applications (MIT) 14.451 Dynamic Optimization Methods with Applications (MIT)

Description

This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes. This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes.

Subjects

vector spaces | vector spaces | principle of optimality | principle of optimality | concavity of the value function | concavity of the value function | differentiability of the value function | differentiability of the value function | Euler equations | Euler equations | deterministic dynamics | deterministic dynamics | models with constant returns to scale | models with constant returns to scale | nonstationary models | nonstationary models | stochastic dynamic programming | stochastic dynamic programming | stochastic Euler equations | stochastic Euler equations | stochastic dynamics | stochastic dynamics | calculus of variations | calculus of variations | the maximum principle | the maximum principle | discounted infinite-horizon optimal control | discounted infinite-horizon optimal control | saddle-path stability | saddle-path stability

License

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6.231 Dynamic Programming and Stochastic Control (MIT) 6.231 Dynamic Programming and Stochastic Control (MIT)

Description

This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages (finite and infinite horizon). We will also discuss some approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations. This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages (finite and infinite horizon). We will also discuss some approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.

Subjects

dynamic programming | dynamic programming | stochastic control | stochastic control | decision making | decision making | uncertainty | uncertainty | sequential decision making | sequential decision making | finite horizon | finite horizon | infinite horizon | infinite horizon | approximation methods | approximation methods | state space | state space | large state space | large state space | optimal control | optimal control | dynamical system | dynamical system | dynamic programming and optimal control | dynamic programming and optimal control | deterministic systems | deterministic systems | shortest path | shortest path | state information | state information | rollout | rollout | stochastic shortest path | stochastic shortest path | approximate dynamic programming | approximate dynamic programming

License

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6.253 Convex Analysis and Optimization (MIT) 6.253 Convex Analysis and Optimization (MIT)

Description

6.253 develops the core analytical issues of continuous optimization, duality, and saddle point theory, using a handful of unifying principles that can be easily visualized and readily understood. The mathematical theory of convex sets and functions is discussed in detail, and is the basis for an intuitive, highly visual, geometrical approach to the subject. 6.253 develops the core analytical issues of continuous optimization, duality, and saddle point theory, using a handful of unifying principles that can be easily visualized and readily understood. The mathematical theory of convex sets and functions is discussed in detail, and is the basis for an intuitive, highly visual, geometrical approach to the subject.

Subjects

affine hulls | affine hulls | recession cones | recession cones | global minima | global minima | local minima | local minima | optimal solutions | optimal solutions | hyper planes | hyper planes | minimax theory | minimax theory | polyhedral convexity | polyhedral convexity | polyhedral cones | polyhedral cones | polyhedral sets | polyhedral sets | convex analysis | convex analysis | optimization | optimization | convexity | convexity | Lagrange multipliers | Lagrange multipliers | duality | duality | continuous optimization | continuous optimization | saddle point theory | saddle point theory | linear algebra | linear algebra | real analysis | real analysis | convex sets | convex sets | convex functions | convex functions | extreme points | extreme points | subgradients | subgradients | constrained optimization | constrained optimization | directional derivatives | directional derivatives | subdifferentials | subdifferentials | conical approximations | conical approximations | Fritz John optimality | Fritz John optimality | Exact penalty functions | Exact penalty functions | conjugate duality | conjugate duality | conjugate functions | conjugate functions | Fenchel duality | Fenchel duality | exact penalty functions | exact penalty functions | dual computational methods | dual computational methods

License

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16.323 Principles of Optimal Control (MIT) 16.323 Principles of Optimal Control (MIT)

Description

This course studies basic optimization and the principles of optimal control. It considers deterministic and stochastic problems for both discrete and continuous systems. The course covers solution methods including numerical search algorithms, model predictive control, dynamic programming, variational calculus, and approaches based on Pontryagin's maximum principle, and it includes many examples and applications of the theory. This course studies basic optimization and the principles of optimal control. It considers deterministic and stochastic problems for both discrete and continuous systems. The course covers solution methods including numerical search algorithms, model predictive control, dynamic programming, variational calculus, and approaches based on Pontryagin's maximum principle, and it includes many examples and applications of the theory.

Subjects

nonlinear optimization | nonlinear optimization | dynamic programming | dynamic programming | HJB Equation | HJB Equation | calculus of variations | calculus of variations | constrained optimal control | constrained optimal control | singular arcs | singular arcs | stochastic optimal control | stochastic optimal control | LQG robustness | LQG robustness | feedback control systems | feedback control systems | model predictive control | model predictive control | line search methods | line search methods | Lagrange multipliers | Lagrange multipliers | discrete LQR | discrete LQR

License

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14.471 Public Economics I (MIT) 14.471 Public Economics I (MIT)

Description

This course is a one-semester introduction to the economic analysis of taxation. It covers both theoretical contributions, such as the theory of optimal income and commodity taxation, as well as empirical work, such as the study of how taxes affect labor supply. The course is designed to acquaint students with key questions in the economics of taxation, and to equip them to carry out their own research in this field. This course is a one-semester introduction to the economic analysis of taxation. It covers both theoretical contributions, such as the theory of optimal income and commodity taxation, as well as empirical work, such as the study of how taxes affect labor supply. The course is designed to acquaint students with key questions in the economics of taxation, and to equip them to carry out their own research in this field.

Subjects

economic analysis | economic analysis | taxation | taxation | wealth | wealth | financial policy | financial policy | income | income | investment | investment | asset | asset | political economy | political economy | labor | labor | capital | capital | public policy | public policy | theory | theory | evidence | evidence | government taxation policy | government taxation policy | tax incidence | tax incidence | optimal tax theory | optimal tax theory | labor supply | labor supply | savings | savings | corrective taxes for externalities | corrective taxes for externalities | corporate behavior | corporate behavior | tax expenditure policy | tax expenditure policy | theory of optimal income | theory of optimal income | commodity taxation | commodity taxation | calculus-based microeconomic analysis | calculus-based microeconomic analysis | duality methods | duality methods | household theory | household theory | firm theory | firm theory | growth theory | growth theory

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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11.487 Urban Public Finance in Developing Countries (MIT)

Description

This readings-based course analyzes the structure and operation of government systems in developing countries, with particular emphasis on regional and local governments. Major topics include: the role of decentralization in national economic reform programs; the potential impact of decentralized governments on local economic development; determination of optimal arrangements for sharing fiscal responsibilities among levels of government; evaluation of local revenue and expenditure decisions; and assessment of prospects and options for intergovernmental fiscal reform. Emphasis is on basic economic concerns, with consideration given to political, institutional, and cultural factors.

Subjects

basic economic concerns | political | institutional | and cultural factors | decentralization in national economic reform programs | the potential impact of decentralized governments on local economic development | determination of optimal arrangements for sharing fiscal responsibilities among levels of government | evaluation of local revenue and expenditure decisions | assessment of prospects and options for intergovernmental fiscal reform | political | institutional | and cultural factors | developing countries | public goods | externalities | economic development | balance sheets | fiscal gap | revenues | expenditures | budget deficits | inflation | public finance theory | efficiency | optimal taxation | optimal user fees | basic microeconomic theory | equity | incidence | general equilibrium model | property taxation | tax reform | intergovernmental fiscal relations | fiscal federalism | decentralization | transfers | international lending agencies | programming assistance | conditionalities | public debt | structural adjustment | private sector participation | microfinance

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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6.832 Underactuated Robotics (MIT)

Description

Robots today move far too conservatively, using control systems that attempt to maintain full control authority at all times. Humans and animals move much more aggressively by routinely executing motions which involve a loss of instantaneous control authority. Controlling nonlinear systems without complete control authority requires methods that can reason about and exploit the natural dynamics of our machines. This course discusses nonlinear dynamics and control of underactuated mechanical systems, with an emphasis on machine learning methods. Topics include nonlinear dynamics of passive robots (walkers, swimmers, flyers), motion planning, partial feedback linearization, energy-shaping control, analytical optimal control, reinforcement learning/approximate optimal control, and the influen

Subjects

underactuated robotics | actuated systems | nonlinear dynamics | simple pendulum | optimal control | double integrator | quadratic regulator | Hamilton-Jacobi-Bellman sufficiency | minimum time control | acrobot | cart-pole | partial feedback linearization | energy shaping | policy search | open-loop optimal control | trajectory stabilization | iterative linear quadratic regulator | differential dynamic programming | walking models | rimless wheel | compass gait | kneed compass gait | feedback control | running models | spring-loaded inverted pendulum | Raibert hoppers | motion planning | randomized motion planning | rapidly-exploring randomized trees | probabilistic road maps | feedback motion planning | planning with funnels | linear quadratic regulator | function approximation | state distribution dynamics | state estimation | stochastic optimal control | aircraft | swimming | flapping flight | randomized policy gradient | model-free value methods | temporarl difference learning | Q-learning | actor-critic methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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15.093 Optimization Methods (SMA 5213) (MIT)

Description

This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include the simplex method, network flow methods, branch and bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton's method, heuristic methods, and dynamic programming and optimal control methods. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5213 (Optimisation Methods).

Subjects

principal algorithms | linear | network | discrete | nonlinear | dynamic optimization | optimal control | methodology and the underlying mathematical structures | simplex method | network flow methods | branch and bound and cutting plane methods for discrete optimization | optimality conditions for nonlinear optimization | interior point methods for convex optimization | Newton's method | heuristic methods | dynamic programming | optimal control methods | SMA 5213

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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1.561 Motion Based Design (MIT)

Description

This course presents a rational basis for the preliminary design of motion-sensitive structures. Topics covered include: analytical and numerical techniques for establishing the optimal stiffness distribution, the role of damping in controlling motion, tuned mass dampers, base isolation systems, and active structural control. Examples illustrating the application of the motion-based design paradigm to building structures subjected to seismic excitation are discussed.

Subjects

preliminary design | motion-sensitive structures | analytical techniques | numerical techniques | optimal stiffness distribution | damping | controlling motion | tuned mass dampers | base isolation systems | active structural control | building structures | wind excitation | seismic excitation | building design | numerical analysis | motion control | motion-based design | safety | serviceability | loadings | optimal stiffness | optimal damping | base isolation

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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11.487 Urban Public Finance in Developing Countries (MIT)

Description

This readings-based course analyzes the structure and operation of government systems in developing countries, with particular emphasis on regional and local governments. Major topics include: the role of decentralization in national economic reform programs, the potential impact of decentralized governments on local economic development, determination of optimal arrangements for sharing fiscal responsibilities among levels of government, evaluation of local revenue and expenditure decisions, and assessment of prospects and options for intergovernmental fiscal reform. Emphasis is on basic economic concerns, with consideration given to political, institutional, and cultural factors.

Subjects

basic economic concerns | political | institutional | and cultural factors | decentralization in national economic reform programs | the potential impact of decentralized governments on local economic development | determination of optimal arrangements for sharing fiscal responsibilities among levels of government | evaluation of local revenue and expenditure decisions | assessment of prospects and options for intergovernmental fiscal reform | political | institutional | and cultural factors | developing countries | public goods | externalities | economic development | balance sheets | fiscal gap | revenues | expenditures | budget deficits | inflation | public finance theory | efficiency | optimal taxation | optimal user fees | basic microeconomic theory | equity | incidence | general equilibrium model | property taxation | tax reform | intergovernmental fiscal relations | fiscal federalism | decentralization | transfers | international lending agencies | programming assistance | conditionalities | public debt | structural adjustment | private sector participation | microfinance

License

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14.471 Public Economics I (MIT)

Description

Theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy.

Subjects

economic analysis | taxation | wealth | financial policy | income | investment | asset | political economy | labor | capital | public policy | corporate finance | tax reform | optimal commodity taxes | optimal corrective taxation | optimal stochastic taxes | dynamic consistency issues | debt | equity

License

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1.561 Motion Based Design (MIT)

Description

This course presents a rational basis for the preliminary design of motion-sensitive structures. Topics covered include: analytical and numerical techniques for establishing the optimal stiffness distribution, the role of damping in controlling motion, tuned mass dampers, base isolation systems, and active structural control. Examples illustrating the application of the motion-based design paradigm to building structures subjected to seismic excitation are discussed.

Subjects

preliminary design | motion-sensitive structures | analytical techniques | numerical techniques | optimal stiffness distribution | damping | controlling motion | tuned mass dampers | base isolation systems | active structural control | building structures | wind excitation | seismic excitation | building design | numerical analysis | motion control | motion-based design | safety | serviceability | loadings | optimal stiffness | optimal damping | base isolation

License

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14.471 Public Economics I (MIT)

Description

This course covers theory and evidence on government taxation policy. Topics include tax incidence, optimal tax theory, the effect of taxation on labor supply and savings, taxation and corporate behavior, and tax expenditure policy.

Subjects

economic analysis | taxation | wealth | financial policy | income | investment | asset | political economy | labor | capital | public policy | corporate finance | tax reform | optimal commodity taxes | optimal corrective taxation | optimal stochastic taxes | dynamic consistency issues | debt | equity

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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14.451 Dynamic Optimization Methods with Applications (MIT)

Description

This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes.

Subjects

vector spaces | principle of optimality | concavity of the value function | differentiability of the value function | Euler equations | deterministic dynamics | models with constant returns to scale | nonstationary models | stochastic dynamic programming | stochastic Euler equations | stochastic dynamics | calculus of variations | the maximum principle | discounted infinite-horizon optimal control | saddle-path stability

License

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6.231 Dynamic Programming and Stochastic Control (MIT)

Description

This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages (finite and infinite horizon). We will also discuss some approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.

Subjects

dynamic programming | stochastic control | decision making | uncertainty | sequential decision making | finite horizon | infinite horizon | approximation methods | state space | large state space | optimal control | dynamical system | dynamic programming and optimal control | deterministic systems | shortest path | state information | rollout | stochastic shortest path | approximate dynamic programming

License

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16.888 Multidisciplinary System Design Optimization (MIT) 16.888 Multidisciplinary System Design Optimization (MIT)

Description

This course is mainly focused on the quantitative aspects of design and presents a unifying framework called "Multidisciplinary System Design Optimization" (MSDO). The objective of the course is to present tools and methodologies for performing system optimization in a multidisciplinary design context, focusing on three aspects of the problem: (i) The multidisciplinary character of engineering systems, (ii) design of these complex systems, and (iii) tools for optimization. There is a version of this course (16.60s) offered through the MIT Professional Institute, targeted at professional engineers. This course is mainly focused on the quantitative aspects of design and presents a unifying framework called "Multidisciplinary System Design Optimization" (MSDO). The objective of the course is to present tools and methodologies for performing system optimization in a multidisciplinary design context, focusing on three aspects of the problem: (i) The multidisciplinary character of engineering systems, (ii) design of these complex systems, and (iii) tools for optimization. There is a version of this course (16.60s) offered through the MIT Professional Institute, targeted at professional engineers.

Subjects

optimization | optimization | multidisciplinary design optimization | multidisciplinary design optimization | MDO | MDO | subsystem identification | subsystem identification | interface design | interface design | linear constrained optimization fomulation | linear constrained optimization fomulation | non-linear constrained optimization formulation | non-linear constrained optimization formulation | scalar optimization | scalar optimization | vector optimization | vector optimization | systems engineering | systems engineering | complex systems | complex systems | heuristic search methods | heuristic search methods | tabu search | tabu search | simulated annealing | simulated annealing | genertic algorithms | genertic algorithms | sensitivity | sensitivity | tradeoff analysis | tradeoff analysis | goal programming | goal programming | isoperformance | isoperformance | pareto optimality | pareto optimality | flowchart | flowchart | design vector | design vector | simulation model | simulation model | objective vector | objective vector | input | input | discipline | discipline | output | output | coupling | coupling | multiobjective optimization | multiobjective optimization | optimization algorithms | optimization algorithms | tradespace exploration | tradespace exploration | numerical techniques | numerical techniques | direct methods | direct methods | penalty methods | penalty methods | heuristic techniques | heuristic techniques | SA | SA | GA | GA | approximation methods | approximation methods | sensitivity analysis | sensitivity analysis | isoperformace | isoperformace | output evaluation | output evaluation | MSDO framework | MSDO framework

License

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16.31 Feedback Control Systems (MIT) 16.31 Feedback Control Systems (MIT)

Description

The goal of this subject is to teach the fundamentals of control design and analysis using state-space methods. This includes both the practical and theoretical aspects of the topic. By the end of the course, students should be able to design controllers using state-space methods and evaluate whether these controllers are "robust," that is, if they are likely to work well in practice. The goal of this subject is to teach the fundamentals of control design and analysis using state-space methods. This includes both the practical and theoretical aspects of the topic. By the end of the course, students should be able to design controllers using state-space methods and evaluate whether these controllers are "robust," that is, if they are likely to work well in practice.

Subjects

feedback control | feedback control | feedback control system | feedback control system | state-space | state-space | controllability | controllability | observability | observability | transfer functions | transfer functions | canonical forms | canonical forms | controllers | controllers | pole-placement | pole-placement | optimal control | optimal control | Kalman filter | Kalman filter

License

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14.452 Economic Growth (MIT) 14.452 Economic Growth (MIT)

Description

This half semester class presents an introduction to macroeconomic modeling, focusing on the theory of economic growth and some of its applications. It will introduce a number of models of non-stochastic and stochastic macroeconomic equilibrium. It will use these models to shed light both on the process of economic growth at the world level and on sources of income and growth differences across countries. This half semester class presents an introduction to macroeconomic modeling, focusing on the theory of economic growth and some of its applications. It will introduce a number of models of non-stochastic and stochastic macroeconomic equilibrium. It will use these models to shed light both on the process of economic growth at the world level and on sources of income and growth differences across countries.

Subjects

economic growth | economic growth | development | development | modern | modern | world income distribution | world income distribution | Solow growth model | Solow growth model | income differences | income differences | neoclassical growth | neoclassical growth | optimal and competitive allocations | optimal and competitive allocations | welfare theorems | welfare theorems | overlapping generations | overlapping generations | dynamic efficiency | dynamic efficiency | growth under uncertainty | growth under uncertainty | incomplete markets | incomplete markets | neoclassical endogenous growth | neoclassical endogenous growth | capital accumulation | capital accumulation | externalities | externalities | human capital | human capital | endogenous growth | endogenous growth | expanding input varieties | expanding input varieties | directed technical change | directed technical change | endogenous skill-bias technological change | endogenous skill-bias technological change | endogenous labor-augmenting technological change | endogenous labor-augmenting technological change | interdependences | interdependences | technology diffusion | technology diffusion | open economy | open economy | trade | trade

License

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