A smoothing Levenberg-Marquardt algorithm for semi-infinite programming

被引：10

作者：

Jin, Ping ^{[1
]}

Ling, Chen ^{[1
]}

Shen, Huifei ^{[1
]}

机构：

[1] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Peoples R China

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2015年 / 60卷 / 03期

基金：

美国国家科学基金会;

关键词：

Semi-infinite programming (SIP) problem; KKT system; Nonsmooth equations; Smoothing Levenberg-Marquardt algorithm; Convergence; INEQUALITY CONSTRAINED OPTIMIZATION; NEWTON-TYPE ALGORITHM; VARIATIONAL-INEQUALITIES; ERROR-BOUNDS; SQP METHOD; CONVERGENCE; DISCRETIZATION;

D O I：

10.1007/s10589-014-9698-0

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：

In this paper, we present a smoothing Levenberg-Marquardt algorithm for the solution of the semi-infinite programming (SIP) problem. We first reformulate the KKT system of SIP problem into a system of constrained nonsmooth equations. Then we solve this system by a smoothing Levenberg-Marquardt algorithm. The feasibility is ensured via the aggregated constraint, and at each iteration of the presented algorithm only a quadratic programming has to be solved. Global and local superlinear convergence of this algorithm is established under a local error bound condition, which is much weaker than the nonsingularity condition. Preliminary numerical results are reported.

引用

页码：675 / 695

页数：21

共 32 条

[1] [Anonymous], 2003, SPRING S OPERAT RES
[2] Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities
Chen, X
Qi, L
Sun, D
[J]. MATHEMATICS OF COMPUTATION, 1998, 67 (222) : 519 - 540
[3] Clarke F. H., 1983, OPTIMIZATION NONSMOO
[4] NUMERICAL TREATMENT OF A CLASS OF SEMI-INFINITE PROGRAMMING PROBLEMS
GUSTAFSON, SA
KORTANEK, KO
[J]. NAVAL RESEARCH LOGISTICS, 1973, 20 (03) : 477 - 504
[5] SEMIINFINITE PROGRAMMING - THEORY, METHODS, AND APPLICATIONS
HETTICH, R
KORTANEK, KO
[J]. SIAM REVIEW, 1993, 35 (03) : 380 - 429
[6] A dual parametrization method for convex semi-infinite programming
Ito, S
Liu, Y
Teo, KL
[J]. ANNALS OF OPERATIONS RESEARCH, 2000, 98 (1-4) : 189 - 213
[7] CRITICAL SETS IN PARAMETRIC OPTIMIZATION
JONGEN, HT
JONKER, P
TWILT, F
[J]. MATHEMATICAL PROGRAMMING, 1986, 34 (03) : 333 - 353
[8] RETRACTED: Levenberg-Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints (Retracted Article)
Kanzow, C
Yamashita, N
Fukushima, M
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 173 (02) : 321 - 343
[9] A CENTRAL CUTTING PLANE ALGORITHM FOR CONVEX SEMI-INFINITE PROGRAMMING PROBLEMS
Kortanek, K. O.
No, Hoon
[J]. SIAM JOURNAL ON OPTIMIZATION, 1993, 3 (04) : 901 - 918
[10] ON LINEAR SEMIINFINITE PROGRAMMING-PROBLEMS - AN ALGORITHM
LAI, HC
WU, SY
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1992, 13 (3-4) : 287 - 304

← 1 2 3 4 →