ON OPTIMALITY AND DUALITY FOR GENERALIZED NONDIFFERENTIABLE FRACTIONAL OPTIMIZATION PROBLEMS

Title & Authors
ON OPTIMALITY AND DUALITY FOR GENERALIZED NONDIFFERENTIABLE FRACTIONAL OPTIMIZATION PROBLEMS
Kim, Moon-Hee; Kim, Gwi-Soo;

Abstract
A generalized nondifferentiable fractional optimization problem (GFP), which consists of a maximum objective function defined by finite fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions, is considered. Recently, Kim et al. [Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146] proved optimality theorems and duality theorems for a nondifferentiable multiobjective fractional programming problem (MFP), which consists of a vector-valued function whose components are fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions. In fact if $\small{\overline{x}}$ is a solution of (GFP), then $\small{\overline{x}}$ is a weakly efficient solution of (MFP), but the converse may not be true. So, it seems to be not trivial that we apply the approach of Kim et al. to (GFP). However, modifying their approach, we obtain optimality conditions and duality results for (GFP).
Keywords
fractional optimization problem;weakly efficient solution;optimality condition;duality;
Language
English
Cited by
1.
OPTIMALITY AND DUALITY FOR GENERALIZED NONDIFFERENTIABLE FRACTIONAL PROGRAMMING WITH GENERALIZED INVEXITY,;;

Journal of applied mathematics & informatics, 2010. vol.28. 5_6, pp.1535-1544
1.
OPTIMALITY AND DUALITY FOR NONDIFFERENTIABLE FRACTIONAL PROGRAMMING WITH GENERALIZED INVEXITY, Journal of the Chungcheong Mathematical Society, 2016, 29, 3, 465
2.
On fractional vector optimization over cones with support functions, Journal of Industrial and Management Optimization, 2016, 13, 2, 31
3.
Optimality and duality for minimax fractional programming with support functions under B-(p,r)-Type I assumptions, Mathematical and Computer Modelling, 2013, 57, 5-6, 1083
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