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

被引：20

作者：

Bonnans, J. Frederic ^{[1
,2
]}

de la Vega, Constanza ^{[3
,4
]}

Dupuis, Xavier ^{[1
,2
]}

机构：

[1] Ecole Polytech, Inria Saclay, F-91128 Palaiseau, France

[2] Ecole Polytech, CMAP, F-91128 Palaiseau, France

[3] Consejo Nacl Invest Cient & Tecn, IMAS, RA-1033 Buenos Aires, DF, Argentina

[4] UBA, Dept Matemat, Buenos Aires, DF, Argentina

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2013年 / 159卷 / 01期

关键词：

Optimal control; Integral equations; State constraints; Second-order optimality conditions; MAXIMUM PRINCIPLE; REGULARITY;

D O I：

10.1007/s10957-013-0299-3

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：1 / 40

页数：40

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