On the choice of parameters for the weighting method in vector optimization

被引：41

作者：

Drummond, L. M. Grana

Maculan, N.

Svaiter, B. F.

机构：

[1] UFRJ, FACC, BR-22290240 Rio De Janeiro, Brazil

[2] UFRJ, COPPE, Programa Engn Sistemas Computacao, BR-21945970 Rio De Janeiro, Brazil

[3] Inst Matematica Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil

来源：

MATHEMATICAL PROGRAMMING | 2008年 / 111卷 / 1-2期

关键词：

vector optimization; weak efficiency; scalarization; weighting method; recession cone;

D O I：

10.1007/s10107-006-0071-7

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We present a geometrical interpretation of the weighting method for constrained (finite dimensional) vector optimization. This approach is based on rigid movements which separate the image set from the negative of the ordering cone. We study conditions on the existence of such translations in terms of the boundedness of the scalar problems produced by the weighting method. Finally, using recession cones, we obtain the main result of our work: a sufficient condition under which weighting vectors yield solvable scalar problems.

引用

页码：201 / 216

页数：16

共 15 条

[1] General equilibrium analysis in ordered topological vector spaces [J].

Aliprantis, CD ;

Florenzano, M ;

Tourky, R .

JOURNAL OF MATHEMATICAL ECONOMICS, 2004, 40 (3-4) :247-269

[2]

ALIPRANTIS CD, IN PRESS J MATH EC

[3]

Avriel M., 2003, NONLINEAR PROGRAMMIN

[4]

Bertsekas D, 2003, Convex Analysis and Optimization, V1

[5]

BERTSEKAS DP, 1995, NONLINEAR PROGRAMMIN

[6]

Gass S, 1955, NAVAL RES LOGIST, V2, P618

[7]

Hamel AH, 2004, J CONVEX ANAL, V11, P163

[8]

JAHN J, 1984, MATH PROGRAM, V29, P203, DOI 10.1007/BF02592221

[9]

Luc D. T., 1989, THEORY VECTOR OPTIMI

[10] SCALARIZATION OF VECTOR OPTIMIZATION PROBLEMS [J].

LUC, DT .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1987, 55 (01) :85-102

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