High-order discretization and multigrid solution of elliptic nonlinear constrained optimal control problems

被引：30

作者：

Borzi, A. ^{[1
]}

机构：

[1] Karl Franzens Univ Graz, Inst Math & Wissenschaftliches Rechnen, A-8010 Graz, Austria

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2007年 / 200卷 / 01期

关键词：

optimal control problems; optimality systems; finite differences; multigrid methods;

D O I：

10.1016/j.cam.2005.12.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

High(-mixed)-order finite difference discretization of optimality systems arising from elliptic nonlinear constrained optimal control problems are discussed. For the solution of these systems, an efficient and robust multigrid algorithm is presented. Theoretical and experimental results show the advantages of higher-order discretization and demonstrate that the proposed multigrid scheme is able to solve efficiently constrained optimal control problems also in the limit case of bang-bang control. (c) 2006 Elsevier B.V. All rights reserved.

引用

页码：67 / 85

页数：19

共 30 条

[1]

[Anonymous], THESIS TU BERLIN BER

[2] Error estimates for the numerical approximation of a semilinear elliptic control problem [J].

Arada, N ;

Casas, E ;

Tröltzsch, F .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2002, 23 (02) :201-229

[3]

ARIAN E, 1995, NASA C PUBLICATION, P15

[4] A multigrid scheme for elliptic constrained optimal control problems [J].

Borzì, A ;

Kunisch, K .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2005, 31 (03) :309-333

[5] The numerical solution of the steady state solid fuel ignition model and its optimal control [J].

Borzì, A ;

Kunisch, K .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 22 (01) :263-284

[6] ACCURACY AND CONVERGENCE PROPERTIES OF THE FINITE DIFFERENCE MULTIGRID SOLUTION OF AN OPTIMAL CONTROL OPTIMALITY SYSTEM [J].

Borzi, Alfio ;

Kunisch, Karl ;

Kwak, Do Y. .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2003, 41 (05) :1477-1497

[7] ON FINITE DIFFERENCE ANALOGUE OF ELLIPTIC BOUNDARY PROBLEM WHICH IS NEITHER DIAGONALLY DOMINANT NOR OF NON-NEGATIVE TYPE [J].

BRAMBLE, JH ;

HUBBARD, BE .

JOURNAL OF MATHEMATICS AND PHYSICS, 1964, 43 (02) :117-&

[8] RIGOROUS QUANTITATIVE-ANALYSIS OF MULTIGRID .1. CONSTANT-COEFFICIENTS 2-LEVEL CYCLE WITH L2-NORM [J].

BRANDT, A .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1994, 31 (06) :1695-1730

[9]

BRANDT A, 1977, MATH COMPUT, V31, P333, DOI 10.1090/S0025-5718-1977-0431719-X

[10] MULTIGRID ALGORITHMS FOR THE SOLUTION OF LINEAR COMPLEMENTARITY-PROBLEMS ARISING FROM FREE-BOUNDARY PROBLEMS [J].

BRANDT, A ;

CRYER, CW .

SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1983, 4 (04) :655-684

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