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15.082J Network Optimization (MIT) 15.082J Network Optimization (MIT)

Description

15.082J/6.855J is an H-level graduate subject in the theory and practice of network flows and its extensions. Network flow problems form a subclass of linear programming problems with applications to transportation, logistics, manufacturing, computer science, project management, finance as well as a number of other domains. This subject will survey some of the applications of network flows and focus on key special cases of network flow problems including the following: the shortest path problem, the maximum flow problem, the minimum cost flow problem, and the multi-commodity flow problem. 15.082J/6.855J is an H-level graduate subject in the theory and practice of network flows and its extensions. Network flow problems form a subclass of linear programming problems with applications to transportation, logistics, manufacturing, computer science, project management, finance as well as a number of other domains. This subject will survey some of the applications of network flows and focus on key special cases of network flow problems including the following: the shortest path problem, the maximum flow problem, the minimum cost flow problem, and the multi-commodity flow problem.

Subjects

network flows | network flows | extensions | extensions | network flow problems | network flow problems | transportation | transportation | logistics | logistics | manufacturing | manufacturing | computer science | computer science | project management | project management | finance | finance | the shortest path problem | the shortest path problem | the maximum flow problem | the maximum flow problem | the minimum cost flow problem | the minimum cost flow problem | the multi-commodity flow problem | the multi-commodity flow problem | communication | communication | systems | systems | applications | applications | efficiency | efficiency | algorithms | algorithms | traffic | traffic | equilibrium | equilibrium | design | design | mplementation | mplementation | linear programming | linear programming | implementation | implementation | computer | computer | science | science | linear | linear | programming | programming | network | network | flow | flow | problems | problems | project | project | management | management | maximum | maximum | minimum | minimum | cost | cost | multi-commodity | multi-commodity | shortest | shortest | path | path | 15.082 | 15.082 | 6.855 | 6.855

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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15.083J Integer Programming and Combinatorial Optimization (MIT) 15.083J 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. 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 | 15.083

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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6.251J Introduction to Mathematical Programming (MIT) 6.251J Introduction to Mathematical Programming (MIT)

Description

This course offers an introduction to optimization problems, algorithms, and their complexity, emphasizing basic methodologies and the underlying mathematical structures. The main topics covered include: Theory and algorithms for linear programming Network flow problems and algorithms Introduction to integer programming and combinatorial problems This course offers an introduction to optimization problems, algorithms, and their complexity, emphasizing basic methodologies and the underlying mathematical structures. The main topics covered include: Theory and algorithms for linear programming Network flow problems and algorithms Introduction to integer programming and combinatorial problems

Subjects

optimization | optimization | algorithms | algorithms | linear programming | linear programming | network flow problems | network flow problems | integer programming | integer programming | combinatorial problems | combinatorial problems | mathematics | mathematics | mathematical programming | mathematical programming | 6.251 | 6.251 | 15.081 | 15.081

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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15.084J 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 | 6.252

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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5.08J Biological Chemistry II (MIT) 5.08J Biological Chemistry II (MIT)

Description

This course deals with a more advanced treatment of the biochemical mechanisms that underlie biological processes. Emphasis will be given to the experimental methods used to unravel how these processes fit into the cellular context as well as the coordinated regulation of these processes. Topics include macromolecular machines for energy and force transduction, regulation of biosynthetic and degradative pathways, and the structure and function of nucleic acids. This course deals with a more advanced treatment of the biochemical mechanisms that underlie biological processes. Emphasis will be given to the experimental methods used to unravel how these processes fit into the cellular context as well as the coordinated regulation of these processes. Topics include macromolecular machines for energy and force transduction, regulation of biosynthetic and degradative pathways, and the structure and function of nucleic acids.

Subjects

biochemistry | biochemistry | biological chemistry | biological chemistry | Rasmol | Rasmol | Deep Viewer | Deep Viewer | CHIME | CHIME | BLAST | BLAST | PDB | PDB | macromolecular machines | macromolecular machines | protein folding | protein folding | protein degradation | protein degradation | fatty acid synthases | fatty acid synthases | polyketide synthases | polyketide synthases | non-ribosomal polypeptide synthases | non-ribosomal polypeptide synthases | metal homeostasis | metal homeostasis | biochemical mechanisms | biochemical mechanisms | biochemical pathways | biochemical pathways | macromolecular interactions | macromolecular interactions | ribosome | ribosome | mRNA | mRNA | metabolic networking | metabolic networking | 5.08 | 5.08 | 7.08 | 7.08

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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6.252J 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 | 15.084

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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15.082J Network Optimization (MIT) 15.082J Network Optimization (MIT)

Description

15.082J/6.855J/ESD.78J is a graduate subject in the theory and practice of network flows and its extensions. Network flow problems form a subclass of linear programming problems with applications to transportation, logistics, manufacturing, computer science, project management, and finance, as well as a number of other domains. This subject will survey some of the applications of network flows and focus on key special cases of network flow problems including the following: the shortest path problem, the maximum flow problem, the minimum cost flow problem, and the multi-commodity flow problem. We will also consider other extensions of network flow problems. 15.082J/6.855J/ESD.78J is a graduate subject in the theory and practice of network flows and its extensions. Network flow problems form a subclass of linear programming problems with applications to transportation, logistics, manufacturing, computer science, project management, and finance, as well as a number of other domains. This subject will survey some of the applications of network flows and focus on key special cases of network flow problems including the following: the shortest path problem, the maximum flow problem, the minimum cost flow problem, and the multi-commodity flow problem. We will also consider other extensions of network flow problems.

Subjects

15.082 | 15.082 | 6.855 | 6.855 | ESD.78 | ESD.78 | network models | network models | network design | network design | maximum flow algorithm | maximum flow algorithm | minimum cost flow | minimum cost flow | shortest path algorithm | shortest path algorithm | algorithm efficiency | algorithm efficiency | preflow push algorithm | preflow push algorithm | data structures | data structures

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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5.08J Biological Chemistry II (MIT)

Description

This course deals with a more advanced treatment of the biochemical mechanisms that underlie biological processes. Emphasis will be given to the experimental methods used to unravel how these processes fit into the cellular context as well as the coordinated regulation of these processes. Topics include macromolecular machines for energy and force transduction, regulation of biosynthetic and degradative pathways, and the structure and function of nucleic acids.

Subjects

biochemistry | biological chemistry | Rasmol | Deep Viewer | CHIME | BLAST | PDB | macromolecular machines | protein folding | protein degradation | fatty acid synthases | polyketide synthases | non-ribosomal polypeptide synthases | metal homeostasis | biochemical mechanisms | biochemical pathways | macromolecular interactions | ribosome | mRNA | metabolic networking | 5.08 | 7.08

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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15.084J Nonlinear Programming (MIT)

Description

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

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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15.082J Network Optimization (MIT)

Description

15.082J/6.855J is an H-level graduate subject in the theory and practice of network flows and its extensions. Network flow problems form a subclass of linear programming problems with applications to transportation, logistics, manufacturing, computer science, project management, finance as well as a number of other domains. This subject will survey some of the applications of network flows and focus on key special cases of network flow problems including the following: the shortest path problem, the maximum flow problem, the minimum cost flow problem, and the multi-commodity flow problem.

Subjects

network flows | extensions | network flow problems | transportation | logistics | manufacturing | computer science | project management | finance | the shortest path problem | the maximum flow problem | the minimum cost flow problem | the multi-commodity flow problem | communication | systems | applications | efficiency | algorithms | traffic | equilibrium | design | mplementation | linear programming | implementation | computer | science | linear | programming | network | flow | problems | project | management | maximum | minimum | cost | multi-commodity | shortest | path | 15.082 | 6.855

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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15.083J 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 | 15.083

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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6.251J Introduction to Mathematical Programming (MIT)

Description

This course offers an introduction to optimization problems, algorithms, and their complexity, emphasizing basic methodologies and the underlying mathematical structures. The main topics covered include: Theory and algorithms for linear programming Network flow problems and algorithms Introduction to integer programming and combinatorial problems

Subjects

optimization | algorithms | linear programming | network flow problems | integer programming | combinatorial problems | mathematics | mathematical programming | 6.251 | 15.081

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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15.082J Network Optimization (MIT)

Description

15.082J/6.855J/ESD.78J is a graduate subject in the theory and practice of network flows and its extensions. Network flow problems form a subclass of linear programming problems with applications to transportation, logistics, manufacturing, computer science, project management, and finance, as well as a number of other domains. This subject will survey some of the applications of network flows and focus on key special cases of network flow problems including the following: the shortest path problem, the maximum flow problem, the minimum cost flow problem, and the multi-commodity flow problem. We will also consider other extensions of network flow problems.

Subjects

15.082 | 6.855 | ESD.78 | network models | network design | maximum flow algorithm | minimum cost flow | shortest path algorithm | algorithm efficiency | preflow push algorithm | data structures

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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15.084J Nonlinear Programming (MIT)

Description

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

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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5.08J Biological Chemistry II (MIT)

Description

This course deals with a more advanced treatment of the biochemical mechanisms that underlie biological processes. Emphasis will be given to the experimental methods used to unravel how these processes fit into the cellular context as well as the coordinated regulation of these processes. Topics include macromolecular machines for energy and force transduction, regulation of biosynthetic and degradative pathways, and the structure and function of nucleic acids.

Subjects

biochemistry | biological chemistry | Rasmol | Deep Viewer | CHIME | BLAST | PDB | macromolecular machines | protein folding | protein degradation | fatty acid synthases | polyketide synthases | non-ribosomal polypeptide synthases | metal homeostasis | biochemical mechanisms | biochemical pathways | macromolecular interactions | ribosome | mRNA | metabolic networking | 5.08 | 7.08

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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6.252J 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.

Subjects

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

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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