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

被引：20

作者：

Kien, B. T. ^{[1
]}

Nhu, V. H. ^{[2
]}

Son, N. H. ^{[3
]}

机构：

[1] Vietnam Acad Sci & Technol, Inst Math, Dept Optimizat & Control Theory, 18 Hoang Quoc Viet Rd, Hanoi, Vietnam

[2] Posts & Telecommun Inst Technol, Dept Sci Fundamentals, Hanoi, Vietnam

[3] Hanoi Univ Sci & Technol, Sch Appl Math & Informat, 1 Dai Co Viet, Hanoi, Vietnam

来源：

SET-VALUED AND VARIATIONAL ANALYSIS | 2017年 / 25卷 / 01期

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; CONTROL-STATE CONSTRAINTS; REGULARITY; EQUATIONS;

D O I：

10.1007/s11228-016-0373-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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：34

共 27 条

[1] Adams R.A., 1975, Sobolev Spaces
[2] [Anonymous], 1990, OPTIMIZATION NONSMOO
[3] Aubin JP., 1990, SET VALUED ANAL
[4] Bayen T, 2014, T AM MATH SOC, V366, P2063
[5] Bonnans J.F., 2013, PERTURBATION ANAL OP
[6] No-gap second-order optimality conditions for optimal control problems with a single state constraint and control
Bonnans, J. Frederic
Hermant, Audrey
[J]. MATHEMATICAL PROGRAMMING, 2009, 117 (1-2) : 21 - 50
[7] Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints
Bonnans, J. Frederic
Hermant, Audrey
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2009, 26 (02): : 561 - 598
[8] Optimal control problems with partially polyhedric constraints
Bonnans, JF
Zidani, H
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (06) : 1726 - 1741
[9] Second-order analysis for control constrained optimal control problems of semilinear elliptic systems
Bonnans, JF
[J]. APPLIED MATHEMATICS AND OPTIMIZATION, 1998, 38 (03) : 303 - 325
[10] BREZIS H, 1972, J MATH PURE APPL, V51, P1

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