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2013
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# Ivan Beschastnyi

SISSA

## Publications:

 Agrachev A., Beschastnyi I. Symplectic Geometry of Constrained Optimization 2017, vol. 22, no. 6, pp.  750–770 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. Keywords: optimal control, second variation, Lagrangian Grassmanian, Maslov index Citation: Agrachev A., Beschastnyi I.,  Symplectic Geometry of Constrained Optimization, Regular and Chaotic Dynamics, 2017, vol. 22, no. 6, pp. 750–770 DOI:10.1134/S1560354717060119