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

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.
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https://hal.inria.fr/hal-00825273
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Submitted on : Thursday, May 23, 2013 - 12:36:58 PM
Last modification on : Wednesday, November 10, 2021 - 10:18:03 AM
Long-term archiving on: : Saturday, August 24, 2013 - 5:20:30 AM

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J. Frederic Bonnans, Xavier Dupuis, Laurent Pfeiffer. Second-order necessary conditions in Pontryagin form for optimal control problems. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (6), pp.3887-3916. ⟨10.1137/130923452⟩. ⟨hal-00825273⟩

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