Tikhonov-type regularization method for efficient solutions in vector optimization

被引：1

作者：

Thai Doan Chuong ^{[1
]}

机构：

[1] Dong Thap Univ, Dept Math, Cao Lanh City, Dong Thap Prov, Vietnam

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 234卷 / 03期

关键词：

Vector optimization; Efficient solution; Tikhonov-type regularization method; Asymptotic function; Asymptotic cone; PROXIMAL METHODS;

D O I：

10.1016/j.cam.2010.01.040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper is devoted to developing the Tikhonov-type regularization algorithm of finding efficient solutions to the vector optimization problem for a mapping between finite dimensional Hilbert spaces with respect to the partial order induced by a pointed closed convex cone. We prove that under some suitable conditions either the sequence generated by our method converges to an efficient solution or all of its cluster points belong to the set of all efficient solutions of this problem. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：761 / 766

页数：6

共 16 条

[1]

[Anonymous], 2005, MULTICRITERIA OPTIMI

[2]

AUSLENDER A, 2003, SPRINGER MG MATH, pR7

[3] Approximate efficiency rand scalar stationarity in unbounded nonsmooth convex vector optimization problems [J].

Bolintinéanu, S .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2000, 106 (02) :265-296

[4]

Bonnans J.F., 2013, PERTURBATION ANAL OP

[5] Proximal methods in vector optimization [J].

Bonnel, H ;

Iusem, AN ;

Svaiter, BF .

SIAM JOURNAL ON OPTIMIZATION, 2005, 15 (04) :953-970

[6] Approximate proximal methods in vector optimization [J].

Ceng, Lu-Chuan ;

Yao, Jen-Chih .

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2007, 183 (01) :1-19

[7] Convergence analysis of Tikhonov-type regularization algorithms for multiobjective optimization problems [J].

Chen, Zhe ;

Xiang, Changhe ;

Zhao, Kequan ;

Liu, Xuewen .

APPLIED MATHEMATICS AND COMPUTATION, 2009, 211 (01) :167-172

[8]

CHUONG TD, HYBRID APPROXI UNPUB

[9]

CHUONG TD, STEEPEST DESCE UNPUB

[10] On the choice of parameters for the weighting method in vector optimization [J].

Drummond, L. M. Grana ;

Maculan, N. ;

Svaiter, B. F. .

MATHEMATICAL PROGRAMMING, 2008, 111 (1-2) :201-216

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