Variational Approach to Second-Order Optimality Conditions for Control Problems with Pure State Constraints

Daniel Hoehener 1
1 C&O - Equipe combinatoire et optimisation
UPMC - Université Pierre et Marie Curie - Paris 6, CNRS - Centre National de la Recherche Scientifique : FRE3232
Abstract : For optimal control problems with set-valued control constraints and pure state constraints we propose new second-order necessary optimality conditions. In addition to the usual second-order derivative of the Hamiltonian, these conditions contain extra terms involving second-order tangents to the set of feasible trajectory-control pairs at the extremal process under consideration. The second-order necessary optimality conditions of the present work are obtained by using a variational approach. In particular, we present a new second-order variational equation. This approach allows us to make direct proofs as opposed to the classical way of obtaining second-order necessary conditions by using an abstract infinite dimensional optimization problem. No convexity assumptions on the constraints are imposed and optimal controls are required to be merely measurable.
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Article dans une revue
SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2012, 50 (3), pp.1139-1173. 〈10.1137/110828320〉
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https://hal.inria.fr/hal-00800528
Contributeur : Estelle Bouzat <>
Soumis le : mercredi 13 mars 2013 - 19:12:45
Dernière modification le : mercredi 21 mars 2018 - 18:57:28

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Daniel Hoehener. Variational Approach to Second-Order Optimality Conditions for Control Problems with Pure State Constraints. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2012, 50 (3), pp.1139-1173. 〈10.1137/110828320〉. 〈hal-00800528〉

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