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.

Symplectic geometry of constrained optimization / Agrachev, Andrey; Beschastnyi, Ivan. - In: REGULAR & CHAOTIC DYNAMICS. - ISSN 1560-3547. - 22:6(2017), pp. 750-770. [10.1134/S1560354717060119]

Symplectic geometry of constrained optimization

Agrachev, Andrey;Beschastnyi, Ivan
2017

Abstract

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.
22
6
750
770
https://arxiv.org/abs/1705.06103
https://link.springer.com/article/10.1134%2FS1560354717060119
Agrachev, Andrey; Beschastnyi, Ivan
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/63345
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