Theorems of the alternative and optimization with set-valued maps

X. M. Yang; Xiaoqi Yang; G. Y. Chen

doi:10.1023/A:1026407517917

Theorems of the alternative and optimization with set-valued maps

X. M. Yang
, Xiaoqi Yang
, G. Y. Chen

Research output: Journal article publication › Journal article › Academic research › peer-review

56 Citations (Scopus)

Abstract

In this paper, the concept of generalized cone subconvexlike set-valued maps is presented and a theorem of alternative for the system of generalized inequality-equality set-valued maps is established. By applying the theorem of the alternative and other results, necessary and sufficient optimality conditions for vector optimization problems with generalized cone subconvexlike set-valued maps are obtained.

Original language	English
Pages (from-to)	627-640
Number of pages	14
Journal	Journal of Optimization Theory and Applications
Volume	107
Issue number	3
DOIs	https://doi.org/10.1023/A:1026407517917
Publication status	Published - 1 Jan 2000

Keywords

Equivalent conditions
Generalized convexity
Optimality conditions
Set-valued maps
Theorem of the alternatives
Vector optimization

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

More information

10.1023/A:1026407517917

Cite this

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N2 - In this paper, the concept of generalized cone subconvexlike set-valued maps is presented and a theorem of alternative for the system of generalized inequality-equality set-valued maps is established. By applying the theorem of the alternative and other results, necessary and sufficient optimality conditions for vector optimization problems with generalized cone subconvexlike set-valued maps are obtained.

AB - In this paper, the concept of generalized cone subconvexlike set-valued maps is presented and a theorem of alternative for the system of generalized inequality-equality set-valued maps is established. By applying the theorem of the alternative and other results, necessary and sufficient optimality conditions for vector optimization problems with generalized cone subconvexlike set-valued maps are obtained.

KW - Equivalent conditions

KW - Generalized convexity

KW - Optimality conditions

KW - Set-valued maps

KW - Theorem of the alternatives

KW - Vector optimization

UR - https://www.scopus.com/pages/publications/0034563707

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DO - 10.1023/A:1026407517917

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JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 3

ER -

Theorems of the alternative and optimization with set-valued maps

Abstract

Keywords

ASJC Scopus subject areas

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