## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2013, Special Issue (2012), Article ID 527183, 5 pages.

### New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem

#### Abstract

We study a nondifferentiable fractional programming problem as follows: $(P){\mathrm{min}}_{x\in K}f(x)/g(x)$ subject to $x\in K\subseteq X,\mathrm{ }{h}_{i}(x)\le 0,\mathrm{ }i=1,2,\dots ,m$, where $K$ is a semiconnected subset in a locally convex topological vector space $X$, $f:K\to \Bbb R$, $g:K\to {\Bbb R}_{+}$ and ${h}_{i}:K\to \Bbb R$, $i=1,2,\dots ,m$. If $f$, $-g$, and ${h}_{i}$, $i=1,2,\dots ,m$, are arc-directionally differentiable, semipreinvex maps with respect to a continuous map $\gamma :[0,1]\to K\subseteq X$ satisfying $\gamma (0)=0$ and ${\gamma }^{\prime }({0}^{+})\in K$, then the necessary and sufficient conditions for optimality of $(P)$ are established.

#### Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2012), Article ID 527183, 5 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394807661

Digital Object Identifier
doi:10.1155/2013/527183

Mathematical Reviews number (MathSciNet)
MR3032201

Zentralblatt MATH identifier
1266.90146

#### Citation

Chen, Yi-Chou; Du, Wei-Shih. New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem. J. Appl. Math. 2013, Special Issue (2012), Article ID 527183, 5 pages. doi:10.1155/2013/527183. https://projecteuclid.org/euclid.jam/1394807661

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