Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(3): 777-786

Printed May 31, 2013

https://doi.org/10.4134/BKMS.2013.50.3.777

Copyright © The Korean Mathematical Society.

Proper efficiency for set-valued optimization problems and vector variational-like inequalities

Xian Jun Long, Jing Quan, and Dao-Jun Wen

Chongqing Technology and Business University, Yibin University, Chongqing Technology and Business University

Abstract

The purpose of this paper is to establish some relationships between proper efficiency of set-valued optimization problems and proper efficiency of vector variational-like inequalities under the assumptions of generalized cone-preinvexity. Our results extend and improve the corresponding results in the literature.

Keywords: set-valued optimization problem, vector variational-like inequality, proper efficiency, contingent epiderivative, generalized cone-preinvexity

MSC numbers: 49J53, 90C26, 90C29

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