Optimization methods — различия между версиями
NATab (обсуждение | вклад) м |
NATab (обсуждение | вклад) м |
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linear algebra and calculus. | linear algebra and calculus. | ||
| − | + | LEcturer: Oleg Khamisov | |
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| + | The course will cover:<br/> | ||
| + | 1.One-dimensional optimization: unimodal functions, convex and quasiconvex functions, zero and first-order methods, local and global minima.<br/> | ||
| + | 2.Existence of solutions: continuous and lower semicontinuous functions, coercive functions, Weierstrass theorem, unique and nonunique solutions.<br/> | ||
| + | 2.Linear optimization: primal and dual linear optimization problems, the simplex methods, interior-point methods, post-optimal analysis.<br/> | ||
| + | 4.Theory of optimality conditions: Fermat principle, the Hessian matrix, positive and negative semidefinite matrices, the Lagrange function and Lagrange multipliers, the Karush-Kuhn-Tucker conditions, regularity, complementarity constraints, stationary points.<br/> | ||
| + | 5.First-order optimization methods: the steepest descent method, conjugate directions, gradient-based methods.<br/> | ||
| + | 6.Second order optimization methods: Newton's method and modifications, trust-region methods.<br/> | ||
| + | 7.Convex optimization: optimality conditions, duality, subgradients and subdifferential, cutting planes and bundle methods, the complexity of convex optimization.<br/> | ||
| + | 8.Decomposition: Dantzig-Wolfe decomposition, Benders decomposition, distributed optimization.<br/> | ||
| + | 9.Conic programming: conic quadratic programming, semidefinite programming, interior point polynomial time methods for conic programming.<br/> | ||
| + | 10.Nonconvex optimization: weakly and d.c. functions, convex envelopes and underestimators, branch and bound technique.<br/> | ||
| + | |||
| + | [https://www.dropbox.com/s/83rudu241umptnz/OptimizationMethods.txt?dl=0 Course Syllabus link] | ||
| + | |||
| + | ===Grading system=== | ||
| + | |||
| + | Grade= 0.600 Control assignments + 0.400 Exam | ||
| + | |||
| + | ===Result Sheet=== | ||
| + | |||
| + | ===Recommended Core Bibliography=== | ||
| + | |||
| + | - Bazaraa M. S., Sherali H.D, Shetty C. M. Nonlinear Programming: Theory and Algorithms 3rd Edition, John Wiley & Sons, 2006 | ||
| + | |||
| + | - Beck, A. First-Order Methods in Optimization, MOS-SIAM Series on Optimization, 2017 | ||
| + | |||
| + | - Ben-Tal A., Arkadi Nemirovski A. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MOS-SIAM Series on Optimization, 2001 | ||
| + | |||
| + | - Nesterov Yu. Introductory Lectures on Convex Optimization, Springer US, 2004 | ||
Версия 12:00, 2 апреля 2021
About the course
The course gives a comprehensive foundation for theory, methods and algorithms of mathematical optimization. The prerequisites are linear algebra and calculus.
LEcturer: Oleg Khamisov
The course will cover:
1.One-dimensional optimization: unimodal functions, convex and quasiconvex functions, zero and first-order methods, local and global minima.
2.Existence of solutions: continuous and lower semicontinuous functions, coercive functions, Weierstrass theorem, unique and nonunique solutions.
2.Linear optimization: primal and dual linear optimization problems, the simplex methods, interior-point methods, post-optimal analysis.
4.Theory of optimality conditions: Fermat principle, the Hessian matrix, positive and negative semidefinite matrices, the Lagrange function and Lagrange multipliers, the Karush-Kuhn-Tucker conditions, regularity, complementarity constraints, stationary points.
5.First-order optimization methods: the steepest descent method, conjugate directions, gradient-based methods.
6.Second order optimization methods: Newton's method and modifications, trust-region methods.
7.Convex optimization: optimality conditions, duality, subgradients and subdifferential, cutting planes and bundle methods, the complexity of convex optimization.
8.Decomposition: Dantzig-Wolfe decomposition, Benders decomposition, distributed optimization.
9.Conic programming: conic quadratic programming, semidefinite programming, interior point polynomial time methods for conic programming.
10.Nonconvex optimization: weakly and d.c. functions, convex envelopes and underestimators, branch and bound technique.
Grading system
Grade= 0.600 Control assignments + 0.400 Exam
Result Sheet
Recommended Core Bibliography
- Bazaraa M. S., Sherali H.D, Shetty C. M. Nonlinear Programming: Theory and Algorithms 3rd Edition, John Wiley & Sons, 2006
- Beck, A. First-Order Methods in Optimization, MOS-SIAM Series on Optimization, 2017
- Ben-Tal A., Arkadi Nemirovski A. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MOS-SIAM Series on Optimization, 2001
- Nesterov Yu. Introductory Lectures on Convex Optimization, Springer US, 2004
