SECOND-ORDER AND STABILITY ANALYSIS FOR STATE-CONSTRAINED ELLIPTIC OPTIMAL CONTROL PROBLEMS WITH SPARSE CONTROLS

被引：19

作者：

Casas, Eduardo ^{[1
]}

Troeltzsch, Fredi ^{[2
]}

机构：

[1] Univ Cantabria, ETSI Ind & Telecomunicac, Dept Matemat Aplicada & Ciencias Computac, E-39005 Santander, Spain

[2] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2014年 / 52卷 / 02期

关键词：

optimal control; semilinear elliptic partial differential equation; pointwise state constraints; sparse control; first- and second-order optimality conditions; stability analysis; MEASURE-SPACES; ERROR ANALYSIS; APPROXIMATION; EQUATIONS;

D O I：

10.1137/130917314

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

An optimal control problem for a semilinear elliptic partial differential equation is discussed subject to pointwise control constraints on the control and the state. The main novelty of the paper is the presence of the L-1-norm of the control as part of the objective functional that eventually leads to sparsity of the optimal control functions. Second-order sufficient optimality conditions are analyzed. They are applied to show the convergence of optimal solutions for vanishing L-2-regularization parameter for the control. The associated convergence rate is estimated.

引用

页码：1010 / 1033

页数：24

共 25 条

[11] SUFFICIENT SECOND-ORDER OPTIMALITY CONDITIONS FOR SEMILINEAR CONTROL PROBLEMS WITH POINTWISE STATE CONSTRAINTS [J].

Casas, Eduardo ;

De Los Reyes, Juan Carlos ;

Troeltzsch, Fredi .

SIAM JOURNAL ON OPTIMIZATION, 2008, 19 (02) :616-643

[12] Sparse Optimal Control of the Schlogl and FitzHugh-Nagumo Systems [J].

Casas, Eduardo ;

Ryll, Christopher ;

Troeltzsch, Fredi .

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 2013, 13 (04) :415-442

[13] OPTIMAL CONTROL OF SEMILINEAR ELLIPTIC EQUATIONS IN MEASURE SPACES [J].

Casas, Eduardo ;

Kunisch, Karl .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2014, 52 (01) :339-364

[14] PARABOLIC CONTROL PROBLEMS IN MEASURE SPACES WITH SPARSE SOLUTIONS [J].

Casas, Eduardo ;

Clason, Christian ;

Kunisch, Karl .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2013, 51 (01) :28-63

[15] Approximation of sparse controls in semilinear equations by piecewise linear functions [J].

Casas, Eduardo ;

Herzog, Roland ;

Wachsmuth, Gerd .

NUMERISCHE MATHEMATIK, 2012, 122 (04) :645-669

[16] SECOND ORDER ANALYSIS FOR BANG-BANG CONTROL PROBLEMS OF PDEs [J].

Casas, Eduardo .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2012, 50 (04) :2355-2372

[17] APPROXIMATION OF ELLIPTIC CONTROL PROBLEMS IN MEASURE SPACES WITH SPARSE SOLUTIONS [J].

Casas, Eduardo ;

Clason, Christian ;

Kunisch, Karl .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2012, 50 (04) :1735-1752

[18] OPTIMALITY CONDITIONS AND ERROR ANALYSIS OF SEMILINEAR ELLIPTIC CONTROL PROBLEMS WITH L1 COST FUNCTIONAL [J].

Casas, Eduardo ;

Herzog, Roland ;

Wachsmuth, Gerd .

SIAM JOURNAL ON OPTIMIZATION, 2012, 22 (03) :795-820

[19]

Clarke F.H, 1983, OPTIMIZATION NONSMOO

[20]

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