Infine Functions, Nonsmooth Alternative Theorems and Vector Optimization Problems |
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Authors: | Pham Huu Sach Gue Myung Lee Do Sang Kim |
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Institution: | (1) Hanoi Institute of Mathematics, P.O. Box 631, Boho, Hanoi, Vietnam;(2) Department of Applied Mathematics, Pukyong National University, Pusan, 608-737, Republic of Korea;Corresponding author; e-mail |
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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. |
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