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Second-order necessary conditions in Pontryagin form for optimal control problems

J. Frederic Bonnans(frederic.bonnans***at***inria.fr)
Xavier Dupuis(xavier.dupuis***at***cmap.polytechnique.fr)
Laurent Pfeiffer(laurent.pfeiffer***at***polytechnique.edu)

Abstract: In this report, we state and prove first- and second-order necessary conditions in Pontryagin form for optimal control problems with pure state and mixed control-state constraints. We say that a Lagrange multiplier of an optimal control problem is a Pontryagin multiplier if it is such that Pontryagin's minimum principle holds, and we call optimality conditions in Pontryagin form those which only involve Pontryagin multipliers. Our conditions rely on a technique of partial relaxation, and apply to Pontryagin local minima.

Keywords: Optimal control; pure state and mixed control-state constraints; Pontryagin's principle; Pontryagin multipliers; second-order necessary conditions; partial relaxation.

Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Published as the Inria Research Report No 3806.

Download: [PDF]

Entry Submitted: 05/23/2013
Entry Accepted: 05/23/2013
Entry Last Modified: 05/23/2013

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