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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 frameworkLicense

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See all metadata15.093J Optimization Methods (MIT) 15.093J Optimization Methods (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 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.Subjects

Linear optimization | Linear optimization | Robust optimization | Robust optimization | Network flows | Network flows | Discrete optimization | Discrete optimization | Dynamic optimization | Dynamic optimization | Nonlinear optimization | Nonlinear optimizationLicense

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The course is a comprehensive introduction to the theory, algorithms and applications of integer optimization and is organized in four parts: formulations and relaxations, algebra and geometry of integer optimization, algorithms for integer optimization, and extensions of integer optimization. The course is a comprehensive introduction to the theory, algorithms and applications of integer optimization and is organized in four parts: formulations and relaxations, algebra and geometry of integer optimization, algorithms for integer optimization, and extensions of integer optimization.Subjects

theory | theory | algorithms | algorithms | integer optimization | integer optimization | formulations and relaxations | formulations and relaxations | algebra and geometry of integer optimization | algebra and geometry of integer optimization | algorithms for integer optimization | algorithms for integer optimization | extensions of integer optimization | extensions of integer optimization | 15.083 | 15.083License

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See all metadata15.093 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 5213License

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See all metadata16.323 Principles of Optimal Control (MIT) 16.323 Principles of Optimal Control (MIT)

Description

This course studies the principles of deterministic optimal control. It uses variational calculus and Pontryagin's maximum principle. It focuses on applications of the theory, including optimal feedback control, time-optimal control, and others. Dynamic programming and numerical search algorithms are introduced briefly. This course studies the principles of deterministic optimal control. It uses variational calculus and Pontryagin's maximum principle. It focuses on applications of the theory, including optimal feedback control, time-optimal control, and others. Dynamic programming and numerical search algorithms are introduced briefly.Subjects

nonlinear optimization | nonlinear optimization | linear quadratic regulators | linear quadratic regulators | MATLAB implementation | MATLAB implementation | dynamic programming | dynamic programming | calculus of variations | calculus of variations | LQR | LQR | LQG | LQG | stochastic optimization | stochastic optimization | on-line optimization and control | on-line optimization and control | constrained optimization | constrained optimization | signals | signals | system norms | system norms | Model Predictive Behavior | Model Predictive Behavior | quadratic programming | quadratic programming | mixed-integer linear programming | mixed-integer linear programming | linear programming | linear programmingLicense

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This course is an introduction to linear optimization and its extensions emphasizing the underlying mathematical structures, geometrical ideas, algorithms and solutions of practical problems. The topics covered include: formulations, the geometry of linear optimization, duality theory, the simplex method, sensitivity analysis, robust optimization, large scale optimization network flows, solving problems with an exponential number of constraints and the ellipsoid method, interior point methods, semidefinite optimization, solving real world problems problems with computer software, discrete optimization formulations and algorithms. This course is an introduction to linear optimization and its extensions emphasizing the underlying mathematical structures, geometrical ideas, algorithms and solutions of practical problems. The topics covered include: formulations, the geometry of linear optimization, duality theory, the simplex method, sensitivity analysis, robust optimization, large scale optimization network flows, solving problems with an exponential number of constraints and the ellipsoid method, interior point methods, semidefinite optimization, solving real world problems problems with computer software, discrete optimization formulations and algorithms.Subjects

Formulations | Formulations | Simplex method | Simplex method | Duality theory | Duality theory | Sensitivity analysis | Sensitivity analysis | Robust optimization | Robust optimization | Large scale optimization | Large scale optimization | Network flows | Network flows | The Ellipsoid method | The Ellipsoid method | Interior point methods | Interior point methods | Semidefinite optimization | Semidefinite optimization | Discrete optimization | Discrete optimizationLicense

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See all metadata6.252J Nonlinear Programming (MIT) 6.252J Nonlinear Programming (MIT)

Description

6.252J is a course in the department's "Communication, Control, and Signal Processing" concentration. This course provides a unified analytical and computational approach to nonlinear optimization problems. The topics covered in this course include: unconstrained optimization methods, constrained optimization methods, convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. There is also a comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory. Throughout the course, applications are drawn from control, communications, power systems, and resource allocation problems. 6.252J is a course in the department's "Communication, Control, and Signal Processing" concentration. This course provides a unified analytical and computational approach to nonlinear optimization problems. The topics covered in this course include: unconstrained optimization methods, constrained optimization methods, convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. There is also a comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory. Throughout the course, applications are drawn from control, communications, power systems, and resource allocation problems.Subjects

nonlinear programming | nonlinear programming | non-linear programming | non-linear programming | nonlinear optimization | nonlinear optimization | unconstrained optimization | unconstrained optimization | gradient | gradient | conjugate direction | conjugate direction | Newton | Newton | quasi-Newton methods | quasi-Newton methods | constrained optimization | constrained optimization | feasible directions | feasible directions | projection | projection | interior point | interior point | Lagrange multiplier | Lagrange multiplier | convex analysis | convex analysis | Lagrangian relaxation | Lagrangian relaxation | nondifferentiable optimization | nondifferentiable optimization | integer programming | integer programming | optimality conditions | optimality conditions | Lagrange multiplier theory | Lagrange multiplier theory | duality theory | duality theory | control | control | communications | communications | power systems | power systems | resource allocation | resource allocation | 6.252 | 6.252 | 15.084 | 15.084License

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See all metadata15.099 Readings in Optimization (MIT) 15.099 Readings in Optimization (MIT)

Description

In keeping with the tradition of the last twenty-some years, the Readings in Optimization seminar will focus on an advanced topic of interest to a portion of the MIT optimization community: randomized methods for deterministic optimization. In contrast to conventional optimization algorithms whose iterates are computed and analyzed deterministically, randomized methods rely on stochastic processes and random number/vector generation as part of the algorithm and/or its analysis. In the seminar, we will study some very recent papers on this topic, many by MIT faculty, as well as some older papers from the existing literature that are only now receiving attention. In keeping with the tradition of the last twenty-some years, the Readings in Optimization seminar will focus on an advanced topic of interest to a portion of the MIT optimization community: randomized methods for deterministic optimization. In contrast to conventional optimization algorithms whose iterates are computed and analyzed deterministically, randomized methods rely on stochastic processes and random number/vector generation as part of the algorithm and/or its analysis. In the seminar, we will study some very recent papers on this topic, many by MIT faculty, as well as some older papers from the existing literature that are only now receiving attention.Subjects

deterministic optimization; algorithms; stochastic processes; random number generation; simplex method; nonlinear; convex; complexity analysis; semidefinite programming; heuristic; global optimization; Las Vegas algorithm; randomized algorithm; linear programming; search techniques; hit and run; NP-hard; approximation | deterministic optimization; algorithms; stochastic processes; random number generation; simplex method; nonlinear; convex; complexity analysis; semidefinite programming; heuristic; global optimization; Las Vegas algorithm; randomized algorithm; linear programming; search techniques; hit and run; NP-hard; approximation | deterministic optimization | deterministic optimization | algorithms | algorithms | stochastic processes | stochastic processes | random number generation | random number generation | simplex method | simplex method | nonlinear | nonlinear | convex | convex | complexity analysis | complexity analysis | semidefinite programming | semidefinite programming | heuristic | heuristic | global optimization | global optimization | Las Vegas algorithm | Las Vegas algorithm | randomized algorithm | randomized algorithm | linear programming | linear programming | search techniques | search techniques | hit and run | hit and run | NP-hard | NP-hard | approximation | approximationLicense

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Includes audio/video content: AV lectures. Modern computing platforms provide unprecedented amounts of raw computational power. But significant complexity comes along with this power, to the point that making useful computations exploit even a fraction of the potential of the computing platform is a substantial challenge. Indeed, obtaining good performance requires a comprehensive understanding of all layers of the underlying platform, deep insight into the computation at hand, and the ingenuity and creativity required to obtain an effective mapping of the computation onto the machine. The reward for mastering these sophisticated and challenging topics is the ability to make computations that can process large amount of data orders of magnitude more quickly and efficiently and to obtain re Includes audio/video content: AV lectures. Modern computing platforms provide unprecedented amounts of raw computational power. But significant complexity comes along with this power, to the point that making useful computations exploit even a fraction of the potential of the computing platform is a substantial challenge. Indeed, obtaining good performance requires a comprehensive understanding of all layers of the underlying platform, deep insight into the computation at hand, and the ingenuity and creativity required to obtain an effective mapping of the computation onto the machine. The reward for mastering these sophisticated and challenging topics is the ability to make computations that can process large amount of data orders of magnitude more quickly and efficiently and to obtain reSubjects

performance analysis | performance analysis | algorithmic techniques | algorithmic techniques | high performance | high performance | instruction level optimization | instruction level optimization | cache optimization | cache optimization | memory optimization | memory optimization | parallel programming | parallel programming | scalable distributed systems | scalable distributed systemsLicense

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.htmSite sourced from

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The course is a comprehensive introduction to the theory, algorithms and applications of integer optimization and is organized in four parts: formulations and relaxations, algebra and geometry of integer optimization, algorithms for integer optimization, and extensions of integer optimization. The course is a comprehensive introduction to the theory, algorithms and applications of integer optimization and is organized in four parts: formulations and relaxations, algebra and geometry of integer optimization, algorithms for integer optimization, and extensions of integer optimization.Subjects

mixed integer optimization | mixed integer optimization | algorithms for integer optimization | algorithms for integer optimization | robust discrete optimization | robust discrete optimizationLicense

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See all metadata15.060 Data, Models, and Decisions (MIT) 15.060 Data, Models, and Decisions (MIT)

Description

This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice. This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice.Subjects

decision analysis | decision analysis | discrete probability distributions | discrete probability distributions | continuous probability distributions | continuous probability distributions | normal probability distribution | normal probability distribution | statistical sampling | statistical sampling | regression models | regression models | linear optimization | linear optimization | nonlinear optimization | nonlinear optimization | discrete optimization | discrete optimizationLicense

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See all metadata15.060 Data, Models, and Decisions (MIT) 15.060 Data, Models, and Decisions (MIT)

Description

This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice. This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice.Subjects

decision analysis | decision analysis | discrete probability distributions | discrete probability distributions | continuous probability distributions | continuous probability distributions | normal probability distribution | normal probability distribution | statistical sampling | statistical sampling | regression models | regression models | linear optimization | linear optimization | nonlinear optimization | nonlinear optimization | discrete optimization | discrete optimizationLicense

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See all metadata15.060 Data, Models, and Decisions (MIT) 15.060 Data, Models, and Decisions (MIT)

Description

This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice. This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice.Subjects

decision analysis | decision analysis | discrete probability distributions | discrete probability distributions | continuous probability distributions | continuous probability distributions | normal probability distribution | normal probability distribution | statistical sampling | statistical sampling | regression models | regression models | linear optimization | linear optimization | nonlinear optimization | nonlinear optimization | discrete optimization | discrete optimizationLicense

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See all metadata15.060 Data, Models, and Decisions (MIT) 15.060 Data, Models, and Decisions (MIT)

Description

This course is designed to introduce first-year Sloan MBA students to the fundamental techniques of using data. In particular, the course focuses on various ways of modeling, or thinking structurally about decision problems in order to make informed management decisions. This course is designed to introduce first-year Sloan MBA students to the fundamental techniques of using data. In particular, the course focuses on various ways of modeling, or thinking structurally about decision problems in order to make informed management decisions.Subjects

decision analysis | decision analysis | discrete probability distributions | discrete probability distributions | continuous probability distributions | continuous probability distributions | normal probability distribution | normal probability distribution | statistical sampling | statistical sampling | regression models | regression models | linear optimization | linear optimization | nonlinear optimization | nonlinear optimization | discrete optimization | discrete optimizationLicense

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.htmSite sourced from

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See all metadata15.060 Data, Models, and Decisions (MIT) 15.060 Data, Models, and Decisions (MIT)

Description

This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice. This course is designed to introduce first-year MBA students to the fundamental quantitative techniques of using data to make informed management decisions. In particular, the course focuses on various ways of modeling, or thinking structurally about, decision problems in order to enhance decision-making skills. Topics include decision analysis, probability, random variables, statistical estimation, regression, simulation, linear optimization, as well as nonlinear and discrete optimization. Management cases are used extensively to illustrate the practical use of modeling tools to improve the management practice.Subjects

decision analysis | decision analysis | discrete probability distributions | discrete probability distributions | continuous probability distributions | continuous probability distributions | normal probability distribution | normal probability distribution | statistical sampling | statistical sampling | regression models | regression models | linear optimization | linear optimization | nonlinear optimization | nonlinear optimization | discrete optimization | discrete optimizationLicense

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.htmSite sourced from

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See all metadata16.888 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.Subjects

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

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See all metadata15.093J Optimization Methods (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.Subjects

Linear optimization | Robust optimization | Network flows | Discrete optimization | Dynamic optimization | Nonlinear optimizationLicense

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See all metadata6.253 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 methodsLicense

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See all metadata15.084J Nonlinear Programming (MIT) 15.084J Nonlinear Programming (MIT)

Description

Includes audio/video content: AV selected lectures. This course introduces students to the fundamentals of nonlinear optimization theory and methods. Topics include unconstrained and constrained optimization, linear and quadratic programming, Lagrange and conic duality theory, interior-point algorithms and theory, Lagrangian relaxation, generalized programming, and semi-definite programming. Algorithmic methods used in the class include steepest descent, Newton's method, conditional gradient and subgradient optimization, interior-point methods and penalty and barrier methods. Includes audio/video content: AV selected lectures. This course introduces students to the fundamentals of nonlinear optimization theory and methods. Topics include unconstrained and constrained optimization, linear and quadratic programming, Lagrange and conic duality theory, interior-point algorithms and theory, Lagrangian relaxation, generalized programming, and semi-definite programming. Algorithmic methods used in the class include steepest descent, Newton's method, conditional gradient and subgradient optimization, interior-point methods and penalty and barrier methods.Subjects

unconstrained and constrained optimization | unconstrained and constrained optimization | Lagrangean relaxation | Lagrangean relaxation | generalized programming | generalized programming | Newton's method | Newton's method | conditional gradient and subgradient optimization | conditional gradient and subgradient optimization | linear and quadratic programming | linear and quadratic programming | lagrange and conic duality theory | lagrange and conic duality theory | interior-point algorithms and theory | interior-point algorithms and theory | semi-definite programming | semi-definite programming | Algorithmic methods include steepest descent | Algorithmic methods include steepest descent | interior-point methods and penalty and barrier methods | interior-point methods and penalty and barrier methods | 15.084 | 15.084 | 6.252 | 6.252License

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This course covers concepts of computation used in analysis of engineering systems. It includes the following topics: data structures, relational database representations of engineering data, algorithms for the solution and optimization of engineering system designs (greedy, dynamic programming, branch and bound, graph algorithms, nonlinear optimization), and introduction to complexity analysis. Object-oriented, efficient implementations of algorithms are emphasized. This course covers concepts of computation used in analysis of engineering systems. It includes the following topics: data structures, relational database representations of engineering data, algorithms for the solution and optimization of engineering system designs (greedy, dynamic programming, branch and bound, graph algorithms, nonlinear optimization), and introduction to complexity analysis. Object-oriented, efficient implementations of algorithms are emphasized.Subjects

databases | databases | data structures | data structures | divide and conquer algorithm | divide and conquer algorithm | greedy algorithm | greedy algorithm | dynamic programming | dynamic programming | branch and bound | branch and bound | linear optimization | linear optimization | nonlinear optimization | nonlinear optimization | approximate queues | approximate queues | network designs | network designsLicense

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See all metadata6.253 Convex Analysis and Optimization (MIT) 6.253 Convex Analysis and Optimization (MIT)

Description

This course will focus on fundamental subjects in convexity, duality, and convex optimization algorithms. The aim is to develop the core analytical and algorithmic issues of continuous optimization, duality, and saddle point theory using a handful of unifying principles that can be easily visualized and readily understood. This course will focus on fundamental subjects in convexity, duality, and convex optimization algorithms. The aim is to develop the core analytical and algorithmic issues of continuous optimization, duality, and saddle point theory using a handful of unifying principles that can be easily visualized and readily understood.Subjects

convex analysis | convex analysis | convex optimization | convex optimization | hyperplanes | hyperplanes | conjugacy | conjugacy | polyhedral convexity | polyhedral convexity | geometric duality | geometric duality | duality theory | duality theory | subgradients | subgradients | optimality conditions | optimality conditions | convex optimization algorithms | convex optimization algorithmsLicense

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.htmSite sourced from

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See all metadataEconomic Applications (Recursive Methods) (MIT) Economic Applications (Recursive Methods) (MIT)

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The unifying theme of this course is best captured by the title of our main reference book: "Recursive Methods in Economic Dynamics". We start by covering deterministic and stochastic dynamic optimization using dynamic programming analysis. We then study the properties of the resulting dynamic systems. Finally, we will go over a recursive method for repeated games that has proven useful in contract theory and macroeconomics. We shall stress applications and examples of all these techniques throughout the course. The unifying theme of this course is best captured by the title of our main reference book: "Recursive Methods in Economic Dynamics". We start by covering deterministic and stochastic dynamic optimization using dynamic programming analysis. We then study the properties of the resulting dynamic systems. Finally, we will go over a recursive method for repeated games that has proven useful in contract theory and macroeconomics. We shall stress applications and examples of all these techniques throughout the course.Subjects

Recursive Methods | Recursive Methods | Economic Dynamics | Economic Dynamics | deterministic dynamic optimization | deterministic dynamic optimization | stochastic dynamic optimization | stochastic dynamic optimization | dynamic programming analysis | dynamic programming analysis | Dynamic systems | Dynamic systems | Repeated games | Repeated games | Macroeconomics | MacroeconomicsLicense

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See all metadata18.433 Combinatorial Optimization (MIT) 18.433 Combinatorial Optimization (MIT)

Description

Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems. Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems.Subjects

linear programming | linear programming | combinatorial optimization | combinatorial optimization | network flow | network flow | matching theory | matching theory | matroid optimization | matroid optimization | approximation algorithms for NP-hard problems | approximation algorithms for NP-hard problems | approximation algorithms | approximation algorithms | NP-hard problems | NP-hard problems | discrete mathematics | discrete mathematics | fundamental algorithmic techniques | fundamental algorithmic techniques | convex programming | convex programming | flow theory | flow theory | randomization | randomizationLicense

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.htmSite sourced from

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See all metadata18.433 Combinatorial Optimization (MIT) 18.433 Combinatorial Optimization (MIT)

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Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems. Combinatorial Optimization provides a thorough treatment of linear programming and combinatorial optimization. Topics include network flow, matching theory, matroid optimization, and approximation algorithms for NP-hard problems.Subjects

linear programming | linear programming | combinatorial optimization | combinatorial optimization | network flow | network flow | matching theory | matching theory | matroid optimization | matroid optimization | approximation algorithms for NP-hard problems | approximation algorithms for NP-hard problems | approximation algorithms | approximation algorithms | NP-hard problems | NP-hard problems | discrete mathematics | discrete mathematics | fundamental algorithmic techniques | fundamental algorithmic techniques | convex programming | convex programming | flow theory | flow theory | randomization | randomizationLicense

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.htmSite sourced from

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See all metadata15.083J Integer Programming and Combinatorial Optimization (MIT)

Description

The course is a comprehensive introduction to the theory, algorithms and applications of integer optimization and is organized in four parts: formulations and relaxations, algebra and geometry of integer optimization, algorithms for integer optimization, and extensions of integer optimization.Subjects

theory | algorithms | integer optimization | formulations and relaxations | algebra and geometry of integer optimization | algorithms for integer optimization | extensions of integer optimization | 15.083License

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.htmSite sourced from

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