Infine Functions, Nonsmooth Alternative Theorems and Vector Optimization Problems

Authors:
Pham Huu Sach;Gue Myung Lee;Do Sang Kim
Affiliations:
Hanoi Institute of Mathematics, P.O. Box 631, Boho, Hanoi, Vietnam/;Department of Applied Mathematics, Pukyong National University, Pusan 608-737, Republic of Korea/Corresponding author/ e-mail: gmlee@pknu.ac.kr);Department of Applied Mathematics, Pukyong National University, Pusan 608-737, Republic of Korea
Venue:
Journal of Global Optimization
Year:
2003

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Abstract

In this paper we introduce a new notion of infine nonsmooth functions and give several characterizations of infineness property. We prove alternative theorems with mixed constraints (i.e., inequality and equality constraints) being described by invex-infine nonsmooth functions. We establish a necessary and sufficient condition for a solution of a vector optimization problem involving mixed constraints to be a properly efficient solution.