A subgradient method for multiobjective optimization

被引：42

作者：

Da Cruz Neto, J. X. ^{[1
]}

Da Silva, G. J. P. ^{[2
]}

Ferreira, O. P. ^{[2
]}

Lopes, J. O. ^{[1
]}

机构：

[1] Univ Fed Piaui, DM, BR-64049500 Teresina, PI, Brazil

[2] Univ Fed Goias, IME, BR-74001970 Goiania, Go, Brazil

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2013年 / 54卷 / 03期

关键词：

Pareto optimality or efficiency; Multiobjective optimization; Subgradient method; Quasi-Fejer convergence;

D O I：

10.1007/s10589-012-9494-7

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：

A method for solving quasiconvex nondifferentiable unconstrained multiobjective optimization problems is proposed in this paper. This method extends to the multiobjective case of the classical subgradient method for real-valued minimization. Assuming the basically componentwise quasiconvexity of the objective components, full convergence (to Pareto optimal points) of all the sequences produced by the method is established.

引用

页码：461 / 472

页数：12

共 20 条

[1]

[Anonymous], 2003, NONLINEAR PROGRAMMIN

[2]

[Anonymous], 1993, CONVEX ANAL MINIMIZA

[3]

Burachik R., 1995, OPTIMIZATION, V32, P137, DOI [DOI 10.1080/02331939508844042, 10.1080/02331939508844042]

[4] Algorithms for the quasiconvex feasibility problem [J].

Censor, Y ;

Segal, A .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 185 (01) :34-50

[5] A steepest descent method for vector optimization [J].

Drummond, LMG ;

Svaiter, BF .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 175 (02) :395-414

[6] A projected gradient method for vector optimization problems [J].

Drummond, LMG ;

Iusem, AN .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2004, 28 (01) :5-29

[7] Steepest descent methods for multicriteria optimization [J].

Fliege, J ;

Svaiter, BF .

MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2000, 51 (03) :479-494

[8]

GAL T, 1997, MULTICRITERIA ANAL, P130, DOI DOI 10.1007/978-3-642-60667-0_14

[9] PROPER EFFICIENCY AND THEORY OF VECTOR MAXIMIZATION [J].

GEOFFRION, AM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1968, 22 (03) :618-+

[10]

Guti?rrez, 1984, REV REAL ACAD CIENC, V78, P523

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