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

  • Joseph Frédéric Bonnans
  • Xavier Dupuis
  • Laurent Pfeiffer
    • Categories Constrained Nonlinear Optimization, Systems governed by Differential Equations Optimization Short URL: https://optimization-online.org/?p=12430

    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.

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    Published as the Inria Research Report No 3806.

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