Optimization methods — различия между версиями
NATab (обсуждение | вклад) м |
NATab (обсуждение | вклад) м |
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| − | + | == About the course == | |
| − | The course gives a comprehensive foundation for theory, methods and algorithms of mathematical optimization. The prerequisites are | + | The course gives a comprehensive foundation for theory, methods and algorithms of mathematical optimization. The prerequisites are linear algebra and calculus. [https://www.hse.ru/ba/data/courses/376703665.html official HSE course page] |
| − | linear algebra and calculus. | + | |
| − | + | ''' Lecturer: [https://www.hse.ru/org/persons/435958676 Oleg Khamisov] ''' | |
| + | |||
| + | 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 txt Course plan] | ||
| + | |||
| + | ==Grading system== | ||
| + | |||
| + | Grade= 0.600 Control assignments + 0.400 Exam | ||
| + | |||
| + | ==Result Sheet== | ||
| + | to be published | ||
| + | |||
| + | ==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 | ||
Текущая версия на 13:55, 9 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. official HSE course page
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
to be published
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
