Second-order necessary conditions in Pontryagin form for optimal control problems
J. Frederic Bonnans(frederic.bonnansinria.fr)
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.
Entry Submitted: 05/23/2013
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