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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
Symplectic Geometry of Constrained Optimization
Andrey A. Agrachevab, I. Yu. Beschastnyib a PSI RAS, ul. Petra I 4a, Pereslavl-Zalessky, 152020 Russia
b SISSA, via Bonomea 265, Trieste, 34136 Italy
Аннотация:
In this paper, we discuss geometric structures related to the Lagrange multipliers rule. The practical goal is to explain how to compute or estimate the Morse index of the second variation. Symplectic geometry allows one to effectively do it even for very degenerate problems with complicated constraints. The main geometric and analytic tool is an appropriately rearranged Maslov index. We try to emphasize the geometric framework and omit analytic routine. Proofs are often replaced with informal explanations, but a well-trained mathematician will easily rewrite them in a conventional way. We believe that Vladimir Arnold would approve of such an attitude.
Ключевые слова:
optimal control, second variation, Lagrangian Grassmanian, Maslov index.
Поступила в редакцию: 10.09.2017 Принята в печать: 07.11.2017
Образец цитирования:
Andrey A. Agrachev, I. Yu. Beschastnyi, “Symplectic Geometry of Constrained Optimization”, Regul. Chaotic Dyn., 22:6 (2017), 750–770
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd277 https://www.mathnet.ru/rus/rcd/v22/i6/p750
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