Geometric Duality for Convex Vector Optimization Problems

被引：0

作者：

Heyde, Frank ^{[1
]}

机构：

[1] Tech Univ Bergakad Freiberg, Fak Math & Informat, D-09596 Freiberg, Germany

来源：

JOURNAL OF CONVEX ANALYSIS | 2013年 / 20卷 / 03期

关键词：

Geometric duality theory; vector optimization; Legendre-Fenchel conjugate; second-order subdifferential; Dupin indicatrix; 2ND DERIVATIVES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This article extends the geometric duality theory to convex vector optimization problems.

引用

页码：813 / 832

页数：20

共 16 条

[1]

[Anonymous], 1970, CONVEX ANAL

[2]

Busemann H., 1958, Interscience Tracts in Pure and Applied Mathematics, V6

[3] RELATIONSHIP BETWEEN 2ND DERIVATIVES OF A CONVEX FUNCTION AND OF ITS CONJUGATE [J].

CROUZEIX, JP .

MATHEMATICAL PROGRAMMING, 1977, 13 (03) :364-365

[4]

Eluzott M., 2012, J GLOBAL OPTIM, V52, P757

[5]

Hamel A. H., 2006, D021 IMPA

[6] GEOMETRIC DUALITY IN MULTIPLE OBJECTIVE LINEAR PROGRAMMING [J].

Heyde, Frank ;

Loehne, Andreas .

SIAM JOURNAL ON OPTIMIZATION, 2008, 19 (02) :836-845

[7]

HIRIARTURRUTY JB, 1989, P LOND MATH SOC, V58, P351

[8]

Löhne A, 2011, VECTOR OPTIM, P1, DOI 10.1007/978-3-642-18351-5

[9]

Lohne A., 2011, ARXIV11075720QFINPR

[10]

Rockafellar R. T., 1998, GRUNDLEHREN MATH WIS, V317

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