OPTIMALITY CONDITIONS FOR SEMI-PREINVEX PROGRAMMING

We consider a semi-preinvex programming as follows: $(P)\left\{ {\begin{array}{*{20}{c}} {\inf f(x)} \\ {subject\,to\,x \in K \subseteq X,g(x) \in - D,} \\ \end{array} } \right\}$ where K is a semi-connected subset; f: K → (Y,C) and g : K → (Z, D) are semi-preinvex maps; while (Y, C) and (Z, D) are...

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Published inTaiwanese journal of mathematics Vol. 1; no. 4; pp. 389 - 404
Main Authors Lai, Hang-Chin, 賴漢卿
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China (Taiwan) 01.12.1997
Subjects
Local minimum
Mathematical functions
Mathematical inequalities
Mathematical theorems
Mathematical vectors
Optimal solutions
Topological vector spaces
Variational inequalities
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Summary:We consider a semi-preinvex programming as follows: $(P)\left\{ {\begin{array}{*{20}{c}} {\inf f(x)} \\ {subject\,to\,x \in K \subseteq X,g(x) \in - D,} \\ \end{array} } \right\}$ where K is a semi-connected subset; f: K → (Y,C) and g : K → (Z, D) are semi-preinvex maps; while (Y, C) and (Z, D) are ordered vector spaces with order cones C and D, respectively. If f and g are arc-directionally differentiable semi-preinvex maps with respect to a continuous map: ϒ : [0,1] → K ⊆ X with ϒ(0) = 0 and ϒˊ (0⁺) = u, then the necessary and sufficient conditions for optimality of (P) is established. It is also established that a solution of an unconstrained semi-preinvex optimization problem is related to a solution of a semi-prevariational inequality .
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500406118