https://www.wikicshse.ru/index.php?action=history&feed=atom&title=Optimization_methodsOptimization methods - История изменений2026-06-06T13:16:11ZИстория изменений этой страницы в викиMediaWiki 1.45.3https://www.wikicshse.ru/index.php?title=Optimization_methods&diff=538&oldid=previmported>NATab: Migrated current public revision from wiki.cs.hse.ru2021-04-09T10:55:44Z<p>Migrated current public revision from wiki.cs.hse.ru</p>
<p><b>Новая страница</b></p><div>== About the course ==<br />
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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]<br />
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''' Lecturer: [https://www.hse.ru/org/persons/435958676 Oleg Khamisov] '''<br />
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The course will cover:<br/><br />
1.One-dimensional optimization: unimodal functions, convex and quasiconvex functions, zero and first-order methods, local and global minima.<br/><br />
2.Existence of solutions: continuous and lower semicontinuous functions, coercive functions, Weierstrass theorem, unique and nonunique solutions.<br/><br />
2.Linear optimization: primal and dual linear optimization problems, the simplex methods, interior-point methods, post-optimal analysis.<br/><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/><br />
5.First-order optimization methods: the steepest descent method, conjugate directions, gradient-based methods.<br/><br />
6.Second order optimization methods: Newton's method and modifications, trust-region methods.<br/><br />
7.Convex optimization: optimality conditions, duality, subgradients and subdifferential, cutting planes and bundle methods, the complexity of convex optimization.<br/><br />
8.Decomposition: Dantzig-Wolfe decomposition, Benders decomposition, distributed optimization.<br/><br />
9.Conic programming: conic quadratic programming, semidefinite programming, interior point polynomial time methods for conic programming.<br/><br />
10.Nonconvex optimization: weakly and d.c. functions, convex envelopes and underestimators, branch and bound technique.<br/><br />
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[https://www.dropbox.com/s/83rudu241umptnz/OptimizationMethods.txt?dl=0 txt Course plan]<br />
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==Grading system==<br />
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Grade= 0.600 Control assignments + 0.400 Exam<br />
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==Result Sheet==<br />
to be published<br />
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==Recommended Core Bibliography==<br />
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- Bazaraa M. S., Sherali H.D, Shetty C. M. Nonlinear Programming: Theory and Algorithms 3rd Edition, John Wiley & Sons, 2006<br />
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- Beck, A. First-Order Methods in Optimization, MOS-SIAM Series on Optimization, 2017<br />
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- Ben-Tal A., Arkadi Nemirovski A. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MOS-SIAM Series on Optimization, 2001<br />
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- Nesterov Yu. Introductory Lectures on Convex Optimization, Springer US, 2004</div>imported>NATab