First- and Second-Order Optimality Conditions for Optimal Control Problems of State Constrained Integral Equations

J. Frédéric Bonnans (), Constanza Vega () and Xavier Dupuis ()
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J. Frédéric Bonnans: Ecole Polytechnique
Constanza Vega: UBA
Xavier Dupuis: Ecole Polytechnique

Journal of Optimization Theory and Applications, 2013, vol. 159, issue 1, No 1, 40 pages

Abstract: Abstract This paper deals with optimal control problems of integral equations, with initial–final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First-order necessary conditions of optimality are given by the description of the set of Lagrange multipliers. Second-order necessary conditions are expressed by the nonnegativity of the supremum of some quadratic forms. Second-order sufficient conditions are also obtained in the case where these quadratic forms are of Legendre type.

Keywords: Optimal control; Integral equations; State constraints; Second-order optimality conditions (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-013-0299-3

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