# Second-order sufficient conditions for strong solutions to optimal control problems

J. Frédéric Bonnans; Xavier Dupuis; Laurent Pfeiffer

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 3, page 704-724
- ISSN: 1292-8119

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topFrédéric Bonnans, J., Dupuis, Xavier, and Pfeiffer, Laurent. "Second-order sufficient conditions for strong solutions to optimal control problems." ESAIM: Control, Optimisation and Calculus of Variations 20.3 (2014): 704-724. <http://eudml.org/doc/272895>.

@article{FrédéricBonnans2014,

abstract = {In this article, given a reference feasible trajectory of an optimal control problem, we say that the quadratic growth property for bounded strong solutions holds if the cost function of the problem has a quadratic growth over the set of feasible trajectories with a bounded control and with a state variable sufficiently close to the reference state variable. Our sufficient second-order optimality conditions in Pontryagin form ensure this property and ensure a fortiori that the reference trajectory is a bounded strong solution. Our proof relies on a decomposition principle, which is a particular second-order expansion of the Lagrangian of the problem.},

author = {Frédéric Bonnans, J., Dupuis, Xavier, Pfeiffer, Laurent},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {optimal control; second-order sufficient conditions; quadratic growth; bounded strong solutions; Pontryagin multipliers; pure state and mixed control-state constraints; decomposition principle; second-order sufficient optimalty conditions},

language = {eng},

number = {3},

pages = {704-724},

publisher = {EDP-Sciences},

title = {Second-order sufficient conditions for strong solutions to optimal control problems},

url = {http://eudml.org/doc/272895},

volume = {20},

year = {2014},

}

TY - JOUR

AU - Frédéric Bonnans, J.

AU - Dupuis, Xavier

AU - Pfeiffer, Laurent

TI - Second-order sufficient conditions for strong solutions to optimal control problems

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2014

PB - EDP-Sciences

VL - 20

IS - 3

SP - 704

EP - 724

AB - In this article, given a reference feasible trajectory of an optimal control problem, we say that the quadratic growth property for bounded strong solutions holds if the cost function of the problem has a quadratic growth over the set of feasible trajectories with a bounded control and with a state variable sufficiently close to the reference state variable. Our sufficient second-order optimality conditions in Pontryagin form ensure this property and ensure a fortiori that the reference trajectory is a bounded strong solution. Our proof relies on a decomposition principle, which is a particular second-order expansion of the Lagrangian of the problem.

LA - eng

KW - optimal control; second-order sufficient conditions; quadratic growth; bounded strong solutions; Pontryagin multipliers; pure state and mixed control-state constraints; decomposition principle; second-order sufficient optimalty conditions

UR - http://eudml.org/doc/272895

ER -

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