## Taiwanese Journal of Mathematics

### OPTIMALITY CONDITIONS FOR SEMI-PREINVEX PROGRAMMING

Hang-Chin Lai

#### Abstract

We consider a semi-preinvex programming as follows: $$(\mbox{P})~~\left\{\begin{array}{l} \inf~f(x)\\ \mbox{ subject to}~x\in K\subseteq X,~g(x)\in -D,\end{array}\right .$$ where $K$ is a semi-connected subset; $f:K\to (Y,C)$ and $g:K\to (Z,D)$ 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: $\gamma :[0,1]\to K\subseteq X$ with $\gamma (0)=0$ and $\gamma '(0^+)=u$, 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 .

#### Article information

Source
Taiwanese J. Math., Volume 1, Number 4 (1997), 389-404.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406118

Digital Object Identifier
doi:10.11650/twjm/1500406118

Mathematical Reviews number (MathSciNet)
MR1486561

Zentralblatt MATH identifier
0894.90164

#### Citation

Lai, Hang-Chin. OPTIMALITY CONDITIONS FOR SEMI-PREINVEX PROGRAMMING. Taiwanese J. Math. 1 (1997), no. 4, 389--404. doi:10.11650/twjm/1500406118. https://projecteuclid.org/euclid.twjm/1500406118