Browse > Article
http://dx.doi.org/10.14403/jcms.2016.29.3.465

OPTIMALITY AND DUALITY FOR NONDIFFERENTIABLE FRACTIONAL PROGRAMMING WITH GENERALIZED INVEXITY  

Kim, Gwi Soo (Department of Applied Mathematics Pukyong National University)
Kim, Moon Hee (Department of Refrigeration Engineering Tongmyong University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.29, no.3, 2016 , pp. 465-475 More about this Journal
Abstract
We establish necessary and sufficient optimality conditions for a class of generalized nondifferentiable fractional optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.
Keywords
fractional optimization problem; optimality theorem; duality;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 R. P. Agarwal, I. Ahmad, and S. Al-Homidan, Optimality and duality for nondifferentiable multiobjective programming problems involving generalized d-$\rho$-(n, ${\theta}$) Type I invex functions, Journal of Nonlinear and Convex Analysis 13 (2012), no. 4, 733-744.
2 I. Ahmad, S. K. Gupta, and A. Jayswal, On sufficiency and duality for non-smooth multiobjective programming problems involving generalized V -r- invex functions, Nonlinear Analysis: Theory, Methods & Applications 74(17) (2011), 5920-5928.   DOI
3 R. P. Agarwal, I. Ahmad, Z. Husain, and A. Jayswal, Optimality and duality in nonsmooth multiobjective optimization involving V -type I invex functions, Journal of Inequalities and Applications 21 (2010).
4 I. Ahmad and S, Sharma, Optimality conditions and duality in nonsmooth multiobjective optimization, Journal of Nonlinear and Convex Analysis 8 (2007), 417-430.
5 F. H. Clarke, Optimization and Nonsmooth Analysis, A Wiley-Interscience Publication, John Wiley & Sons, 1983.
6 D. S. Kim, S. J. Kim, and M. H. Kim, Optimality and duality for a class of nondifferentiable multiobjective fractional programming problems, Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146.   DOI
7 M. H. Kim and G. S Kim, On optimality and duality for generalized nondifferentiable fractional optimization problems, Communications of the Korean Mathematical Society 25 (2010), 139-147.   DOI
8 H. Kuk, G. M. Lee, and D. S. Kim, Nonsmooth multiobjective programs with (V, p)-invexity, Indian Journal of Pure and Applied Mathematics 29 (1998), 405-412.
9 H. Kuk, G. M. Lee, and T. Tanino, Optimality and duality for nonsmooth multiobjective fractional programming with generalized invexity, Journal of Mathematical Analysis and Applications 262 (2001), 365-375.   DOI
10 Z. Liang, H. Huang, and P. M. Pardalos, Optimality conditions and duality for a class of nonlinear fractional programming problems, Journal of Optimization Theory and Applications 110 (2001), 611-619.   DOI
11 M. M. Maklela and P. Neittaanmaki, Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control, World Scientific Publishing Co. Pte. Ltd. 1992.
12 Z. Y. Peng and S. S. Chang, Some properties of semi-G-preinvex functions, Taiwan Journal of Mathematics 17 (2013), no. 3, 873-884.   DOI