Duality in vector optimization with domination structures

被引：0

作者：

Bao T.Q. ^{[1
]}

Le T.T.A.M. ^{[2
,3
]}

Tammer C. ^{[2
]}

Tuan V.A.N.H. ^{[2
]}

机构：

[1] Department of Mathematics and Computer Science, Northern Michigan University

[2] Institute of Mathematics, Faculty of Natural Sciences II, Martin-Luther-University Halle-Wittenberg

[3] Faculty of Basic Sciences, University of Transport and Communications, Hanoi

来源：

Applied Set-Valued Analysis and Optimization | 2019年 / 1卷 / 03期

关键词：

Duality; Nonlinear scalarization function; Variable domination structure; Vector optimization;

D O I：

10.23952/asvao.1.2019.3.06

中图分类号：

学科分类号：

摘要：

In this paper, we study duality schemes for vector optimization problems with respect to variable domination structures by using an appropriate extension of the so-called Gerstewitz nonlinear scalarization function for dealing with weakly nondominated solutions. We apply these results to multiobjective location problems with variable domination structures. For nondominated solutions, we use a general scalarization function which is strictly monotone with respect to the domination structure. The strict monotonicity of our proposed function is also discussed. © 2019 Applied Set-Valued Analysis and Optimization.

引用

页码：319 / 335

页数：16

共 13 条

[1]

Bao T. Q., Eichfelder G., Soleimani B., Tammer C., Ekeland’s variational principle for vector optimization with variable ordering structure, J. Convex Anal, 24, pp. 393-415, (2017)

[2]

Bello Cruz J. Y., Bouza Allende G., A steepest descent-like method for variable order vector optimization problems, J. Optim. Theory Appl, 162, pp. 371-391, (2014)

[3]

Bot R.I., Grad S.M., Wanka G., Duality in Vector Optimization, (2009)

[4]

Doagooei A., Le T.T., Tammer C., Convexity in the framework of variable domination structures and applications in optimization, J. Nonlinear Convex Anal

[5]

Eichfelder G., Ha T.X.D., Optimality conditions for vector optimization problems with variable ordering structures, Optimization, 62, pp. 597-627, (2013)

[6]

Eichfelder G., Variable Ordering Structures in Vector Optimization, (2014)

[7]

Eichfelder G., Vector optimization in medical engineering, Mathematics without boundaries, pp. 181-215, (2014)

[8]

Gerth C., Weidner P., Nonconvex separation theorems and some applications in vector optimization, J. Optim. Theory Appl, 67, pp. 297-320, (1990)

[9]

Gopfert A., Riahi H., Tammer C., Zalinescu C., Variational Methods in Partially Irdered Spaces, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 17, (2003)

[10]

Gopfert A., Riedrichm T., Tammer C., Angewandte Funktionalanalysis, (2009)

← 1 2 →