Characterizations of Approximate Optimality Conditions for Fractional Semi-Infinite Optimization Problems With Uncertainty

FENG Xinyi; SUN Xiangkai

doi:10.21656/1000-0887.420248

Volume 43 Issue 6

Jun. 2022

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2022 > 43(6): 682-689

FENG Xinyi, SUN Xiangkai. Characterizations of Approximate Optimality Conditions for Fractional Semi-Infinite Optimization Problems With Uncertainty[J]. Applied Mathematics and Mechanics, 2022, 43(6): 682-689. doi: 10.21656/1000-0887.420248

Citation:

PDF( 1954 KB)

Characterizations of Approximate Optimality Conditions for Fractional Semi-Infinite Optimization Problems With Uncertainty

doi: 10.21656/1000-0887.420248

FENG Xinyi,
SUN Xiangkai^,

Chongqing Key Laboratory of Social Economy and Applied Statistics, School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P.R.China

Received Date: 2021-08-25
Rev Recd Date: 2021-09-26

Available Online: 2022-04-13

Publish Date: 2022-06-30

Abstract

Abstract

A class of multi-objective fractional semi-infinite optimization problems with uncertain data were investigated. Firstly, a robust optimization model corresponding to the uncertain multi-objective optimization problem was introduced. Then the optimization model was converted to a multi-objective optimization problem with the Dinkelbach method. In turn, by means of the scalarization method, the corresponding scalarization optimization problem was built, and the relationship between robust solutions to the multi-objective optimization problem and its corresponding scalarization optimization problem was described. Finally, through a robust-type sub-differential constraint qualification, the robust optimality condition for approximate quasi-efficient solutions to the multi-objective fractional optimization problem was established.
- multi-objective optimization,
- robust optimization,
- quasi-efficient solution,
- optimality condition

FullText(HTML)

References(21)

References

[1]	DINKELBACH W. On nonlinear fractional programming[J]. Management Science, 1967, 13(7): 492-498. doi: 10.1287/mnsc.13.7.492
[2]	YANG X M, TEO K L, YANG X Q. Symmetric duality for a class of nonlinear fractional programming problems[J]. Journal of Mathematical Analysis and Applications, 2002, 271(1): 7-15. doi: 10.1016/S0022-247X(02)00042-2
[3]	LONG X J, HUANG N J, LIU Z B. Optimality conditions, duality and saddle points for nondifferentiable multiobjective fractional programs[J]. Journal of Industrial and Management Optimization, 2008, 4(2): 287-298. doi: 10.3934/jimo.2008.4.287
[4]	SUN X K, CHAI Y, ZENG J. Farkas-type results for constrained fractional programming with DC functions[J]. Optimization Letters, 2014, 8: 2299-2313. doi: 10.1007/s11590-014-0737-7
[5]	ZHOU Z A, CHEN W. Optimality conditions and duality of the set-valued fractional programming[J]. Pacific Journal of Optimization, 2019, 15(4): 639-651.
[6]	LIU J C, YOKOYAMA K. $ \varepsilon $-optimality and duality for multiobjective fractional programming[J]. Computers and Mathematics With Applications, 1999, 37(8): 119-128. doi: 10.1016/S0898-1221(99)00105-4
[7]	GUPTA P, SHIRAISHI S, YOKOYAMA K. $ \varepsilon $-optimality without constraint qualification for multiobjective fractional problem[J]. Journal of Nonlinear and Convex Analysis, 2005, 6(2): 347-357.
[8]	VERMA R U. Weak $ \varepsilon $-efficiency conditions for multiobjective fractional programming[J]. Applied Mathematics and Computation, 2013, 219(12): 6819-6827. doi: 10.1016/j.amc.2012.12.087
[9]	KIM M H, KIM G S, LEE G M. On $ \varepsilon $-optimality conditions for multiobjective fractional optimization problems[J]. Fixed Point Theory and Applications, 2011, 2011: 6. doi: 10.1186/1687-1812-2011-6
[10]	LI G Y, JEYAKUMAR V, LEE G M. Robust conjugate duality for convex optimization under uncertainty with application to data classification[J]. Nonlinear Analysis, 2011, 74(6): 2327-2341. doi: 10.1016/j.na.2010.11.036
[11]	SUN X K, LI X B, LONG X J, et al. On robust approximate optimal solutions for uncertain convex optimization and applications to multi-objective optimization[J]. Pacific Journal of Optimization, 2017, 13(4): 621-643.
[12]	FAKHAR M, MAHYARINIA M, ZAFARANI J. On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization[J]. European Journal of Operational Research, 2018, 265(1): 39-48. doi: 10.1016/j.ejor.2017.08.003
[13]	SUN X K, TEO K L, ZENG J, et al. Robust approximate optimal solutions for nonlinear semi-infinite programming with uncertainty[J]. Optimization, 2020, 69(9): 2109-2129. doi: 10.1080/02331934.2020.1763990
[14]	赵丹, 孙祥凯. 非凸多目标优化模型的一类鲁棒逼近最优性条件[J]. 应用数学和力学, 2019, 40(6): 694-700. (ZHANG Dan, SUN Xiangkai. Some robust approximate optimality conditions for nonconvex multi-objective optimization problems[J]. Applied Mathematics and Mechanics, 2019, 40(6): 694-700.(in Chinese) ZHANG Dan, SUN Xiangkai. Some robust approximate optimality conditions for nonconvex multi-objective optimization problems[J]. Applied Mathematics and Mechanics, 2019, 40(6): 694-700. (in Chinese))
[15]	LEE J H, LEE G M. On $ \varepsilon $-solutions for robust fractional optimization problems[J]. Journal of Inequalities and Applications, 2014, 2014: 501. doi: 10.1186/1029-242X-2014-501
[16]	ZENG J, XU P, FU H Y. On robust approximate optimal solutions for fractional semi-infinite optimization with uncertainty data[J]. Journal of Inequalities and Applications, 2019, 2019: 45. doi: 10.1186/s13660-019-1997-7
[17]	BEN-TAL A, GHAOUI L E, NEMIROVSKI A. Robust Optimization[M]. Princeton: Princeton University Press, 2009.
[18]	CLARKE F H. Optimization and Nonsmooth Analysis[M]. New York: John Wiley and Sons Inc, 1983.
[19]	ANTCZAK T. Parametric approach for approximate efficiency of robust multiobjective fractional programming problems[J]. Mathematical Methods in Applied Sciences, 2021, 44(14): 11211-11230. doi: 10.1002/mma.7482
[20]	LONG X J, XIAO Y B, HUANG N J. Optimality conditions of approximate solutions for nonsmooth semi-infinite programming problems[J]. Journal of the Operations Research Society of China, 2018, 6(2): 289-299. doi: 10.1007/s40305-017-0167-1
[21]	刘娟, 龙宪军. 非光滑多目标半无限规划问题的混合型对偶[J]. 应用数学和力学, 2021, 42(6): 595-601. (LIU Juan, LONG Xianjun. Mixed type duality for nonsmooth multiobjective semi-infinite programming problems[J]. Applied Mathematics and Mechanics, 2021, 42(6): 595-601.(in Chinese) LIU Juan, LONG Xianjun. Mixed type duality for nonsmooth multiobjective semi-infinite programming problems[J]. Applied Mathematics and Mechanics, 2021, 42(6): 595-601. (in Chinese)