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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L. A. Tuan, Private communication.
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Sach, P.H., Lee, G.M. & Kim, D.S. Infine Functions, Nonsmooth Alternative Theorems and Vector Optimization Problems. Journal of Global Optimization 27, 51–81 (2003). https://doi.org/10.1023/A:1024698418606
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DOI: https://doi.org/10.1023/A:1024698418606