ON OPTIMALITY AND DUALITY FOR GENERALIZED NONDIFFERENTIABLE FRACTIONAL OPTIMIZATION PROBLEMS
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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 ¯x is a solution of (GFP), then ¯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).
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 ¯x is a solution of (GFP), then ¯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).
참고문헌 (11)
- F. H. Clarke, "Optimization and Nonsmooth Analysis, A Wiley-Interscience Publication" (1983), John Wiley & Sons
- D. S. Kim, "Optimality and duality for a class of nondifferentiable multiobjective fractional programming problems", Journal of Optimization Theory and Applications, 129(1), pp.131~146 (2006)
- M. H. Kim, "Non-differentiabel symmetric duality for multiobjective programming with cone constraints", European Journal of Operational Research, 188, pp.652~661 (2008)
- H. Kuk, "nonsmooth multiobjective programs with (V, ½)- invexity", Journal of Pure and Applied Mathematics, 29, pp.405~412 (1998)
- H. Kuk, "Optimality and duality for nonsmooth multiobjective fractional programming with generalized invexity", Journal of Mathematical Analysis and Applications, 262, pp.365~375 (2001)
- Z. Liang, "Optimality conditions and duality for a class of nonlinear fractional programming problems", Journal of Optimization Theory and Applications, 110, pp.611~619 (2001)
- Z. Liang, "Efficiency conditions and duality for a class of multiobjective fractional programming problems", Journal of Global Optimization, 27, pp.444~417 (2003)
- X. J. Long, "Optimality conditions, duality ad saddle points for nondifferentiale multiobjective fractional programs", Journal of Industry Management and Optimization, 4, pp.287~298 (2008)
- M. M. M¨aklel¨a, "Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control" (1992), World Scientific Publishing Co. Pte. Ltd.
- B. Mond, "Nondifferentiable symmetric duality", Bulletine of the Australian Mathematical Society, 53, pp.177~187 (1996)
- X. M. Yang, "Duality and saddle-point type optimality for generalized nonlinear fractional programming", Journal of Mathematical Analysis and Applications, 289, pp.100~109 (2004)