## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2013, Special Issue (2013), Article ID 237428, 7 pages.

### Nonsmooth Multiobjective Fractional Programming with Local Lipschitz Exponential $B\text{-}(p,r)$-Invexity

Shun-Chin Ho

#### Abstract

We study nonsmooth multiobjective fractional programming problem containing local Lipschitz exponential $B\text{-}(p,r)$-invex functions with respect to $\eta$ and $b$. We introduce a new concept of nonconvex functions, called exponential $B\text{-}(p,r)$-invex functions. Base on the generalized invex functions, we establish sufficient optimality conditions for a feasible point to be an efficient solution. Furthermore, employing optimality conditions to perform Mond-Weir type duality model and prove the duality theorems including weak duality, strong duality, and strict converse duality theorem under exponential $B\text{-}(p,r)$-invexity assumptions. Consequently, the optimal values of the primal problem and the Mond-Weir type duality problem have no duality gap under the framework of exponential $B\text{-}(p,r)$-invexity.

#### Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 237428, 7 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394807724

Digital Object Identifier
doi:10.1155/2013/237428

Mathematical Reviews number (MathSciNet)
MR3108952

Zentralblatt MATH identifier
06950571

#### Citation

Ho, Shun-Chin. Nonsmooth Multiobjective Fractional Programming with Local Lipschitz Exponential $B\text{-}(p,r)$ -Invexity. J. Appl. Math. 2013, Special Issue (2013), Article ID 237428, 7 pages. doi:10.1155/2013/237428. https://projecteuclid.org/euclid.jam/1394807724

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