- Volume 25 Issue 1
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ON OPTIMALITY AND DUALITY FOR GENERALIZED NONDIFFERENTIABLE FRACTIONAL OPTIMIZATION PROBLEMS
- Kim, Moon-Hee (Department of Multimedia Engineering, Tongmyong University) ;
- Kim, Gwi-Soo (Department of Applied Mathematics, Pukyong National University)
- Published : 2010.01.31
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
- F. H. Clarke, Optimization and Nonsmooth Analysis, A Wiley-Interscience Publication, John Wiley & Sons, 1983.
- 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. https://doi.org/10.1007/s10957-006-9048-1
- M. H. Kim and D. S. Kim, Non-differentiabel symmetric duality for multiobjective programming with cone constraints, European Journal of Operational Research 188 (2008), 652–661. https://doi.org/10.1016/j.ejor.2007.05.005
H. Kuk, G. M. Lee, and D. S. Kim, nonsmooth multiobjective programs with (V,
$\varphi$)- invexity, Indian Journal of Pure and Applied Mathematics 29 (1998), 405–412.
- 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. https://doi.org/10.1006/jmaa.2001.7586
- 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. https://doi.org/10.1023/A:1017540412396
- Z. Liang, Efficiency conditions and duality for a class of multiobjective fractional programming problems, Journal of Global Optimization 27 (2003), 444–417.
- X. J. Long, N. J. Huang , and Z. B. Liu, Optimality conditions, duality ad saddle points for nondifferentiale multiobjective fractional programs, Journal of Industry Management and Optimization 4 (2008), 287–298. https://doi.org/10.3934/jimo.2008.4.287
- M. M. Maklela and P. Neittaanmaki, Nonsmooth Optimization: Analysis and Algorithms with Applications to Optimal Control, World Scientific Publishing Co. Pte. Ltd. 1992.
- B. Mond and M. Schechter, Nondifferentiable symmetric duality, Bulletine of the Australian Mathematical Society 53 (1996), 177–187. https://doi.org/10.1017/S0004972700016890
- X. M. Yang, X. Q. Yang, and K. L. Teo, Duality and saddle-point type optimality for generalized nonlinear fractional programming, Journal of Mathematical Analysis and Applications 289 (2004), 100–109.
- OPTIMALITY AND DUALITY FOR NONDIFFERENTIABLE FRACTIONAL PROGRAMMING WITH GENERALIZED INVEXITY vol.29, pp.3, 2016, https://doi.org/10.14403/jcms.2016.29.3.465
- Optimality and duality for minimax fractional programming with support functions underB-(p,r)-Type I assumptions vol.57, pp.5-6, 2013, https://doi.org/10.1016/j.mcm.2012.06.028
- On fractional vector optimization over cones with support functions vol.13, pp.2, 2016, https://doi.org/10.3934/jimo.2016031