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. © 2013 Springer Science+Business Media New York.

First- and second-order optimality conditions for optimal control problems of state constrained integral equations / Bonnans, J. Frédéric; De la Vega, Constanza; Dupuis, Xavier. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 159:1(2013), pp. 1-40. [10.1007/s10957-013-0299-3]

First- and second-order optimality conditions for optimal control problems of state constrained integral equations

DUPUIS, XAVIER
2013

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. © 2013 Springer Science+Business Media New York.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/160731
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