Symplectic geometry of constrained optimization

DOI10.1134/S1560354717060119zbMath1408.49043arXiv1705.06103OpenAlexW3103632130MaRDI QIDQ1702816

Andrei A. Agrachev, Ivan Beschastnyi

Publication date: 28 February 2018

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.06103

zbMATH Keywords

optimal controlsecond variationLagrangian multipliersMaslov indexLagrangian Grassmanian

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Symplectic manifolds (general theory) (53D05) Variational problems in a geometric measure-theoretic setting (49Q20) Lagrangian submanifolds; Maslov index (53D12)

Related Items (5)

Index theorems for graph-parametrized optimal control problems ⋮ Operators arising as second variation of optimal control problems and their spectral asymptotics ⋮ Functional determinants for the second variation ⋮ Jacobi fields in optimal control: one-dimensional variations ⋮ Jacobi fields in optimal control: Morse and Maslov indices

Cites Work

• Quadratic mappings in geometric control theory
• Feedback-invariant optimal control theory and differential geometry. II. Jacobi curves for singular extremals
• Pointwise second-order necessary optimality conditions and second-order sensitivity relations in optimal control
• Symplectic geometry and quantum mechanics
• Strong Optimality for a Bang-Bang Trajectory
• Corrigenda to: Introduction to Symplectic Topology
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