Second-Order Optimality Conditions for a Semilinear Elliptic Optimal Control Problem with Mixed Pointwise Constraints

被引：0

作者：

B. T. Kien

V. H. Nhu

N. H. Son

机构：

[1] Institute of Mathematics,Department of Optimization and Control Theory

[2] Vietnam Academy of Science and Technology,Department of Scientific Fundamentals

[3] Posts and Telecommunications Institute of Technology,School of Applied Mathematics and Informatics

[4] Hanoi University of Science and Technology,undefined

来源：

Set-Valued and Variational Analysis | 2017年 / 25卷

关键词：

Second-order necessary optimality condition; Second-order sufficient optimality condition; Optimal control; Semilinear elliptic equation; Mixed pointwise constraint; Strongly extended polyhedricity condition; 49K20; 35J25;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

This paper studies second-order optimality conditions for a semilinear elliptic optimal control problem with mixed pointwise constraints. We show that in some cases, there is a common critical cone under which the second-order necessary and sufficient optimality conditions for the problem are valid. Our results approach to a theory of no-gap second-order conditions. In order to obtain such results, we reduce the problem to a special mathematical programming problem with polyhedricity constraint set. We then use some tools of variational analysis and techniques of semilinear elliptic equations to analyze second-order conditions.

引用

页码：177 / 210

页数：33

共 27 条

[1]

Bayen T(2013)Characterization of locall quadractic growth for strong minima in the optimal control of semilinear elliptic equations Trans. Amer. Math. Soc. 366 2063-2087

[2]

Bonnans JF(1998)Second-order analysis for control constrained optimal control problems of semilinear elliptic systems Appl. Math. Optim. 38 303-325

[3]

Silva FJ(1999)Optimal control problem with partially polyhedric constraints SIAM J. Control Optim. 37 1726-1741

[4]

Bonnans JF(2009)No-gap second-order optimality conditions for optimal control problems with a single state constraint and control Math. Program. Ser. B 117 21-50

[5]

Bonnans JF(2009)Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints Ann. I. H. Poincar - AN 26 561-598

[6]

Zidani H(1972)Problèmes unilatéraux J. Math. Pures Appl. 51 1-168

[7]

Bonnans JF(2012)Second order analysis for bang-bang control problems of PDEs SIAM J. Control Optim. 50 2355-2372

[8]

Hermant A(2008)Sufficient second-order optiMality conditions for semilinear control problems with pointwise state constraints SIAM J. Optim. 19 616-643

[9]

Bonnans JF(2009)First- and second-order optiMality conditions for a class of optimal control problems with quasilinear elliptic equations, SIAM J. Control Optim. 48 688-718

[10]

Hermant A(2002)Second order optiMality conditions for semilinear elliptic control problems with finitely many state constraints SIAM J. Control Optim. 40 1431-1454

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