Some Robust Approximate Optimality Conditions for Nonconvex Multi-Objective Optimization Problems

ZHAO Dan; SUN Xiangkai

doi:10.21656/1000-0887.390289

Volume 40 Issue 6

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2019 > 40(6): 694-700

ZHAO Dan, SUN Xiangkai. Some Robust Approximate Optimality Conditions for Nonconvex Multi-Objective Optimization Problems[J]. Applied Mathematics and Mechanics, 2019, 40(6): 694-700. doi: 10.21656/1000-0887.390289

Citation:

PDF( 326 KB)

Some Robust Approximate Optimality Conditions for Nonconvex Multi-Objective Optimization Problems

doi: 10.21656/1000-0887.390289

ZHAO Dan¹,
SUN Xiangkai²

¹Institute of Applied Mathematics, Zhengzhou Shengda University of Economics, Business & Management, Zhengzhou 451191, P.R.China;²College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P.R.China

Funds: The National Natural Science Foundation of China(11701057)

Received Date: 2018-11-16
Rev Recd Date: 2019-04-10
Publish Date: 2019-06-01

Abstract

Abstract

A class of nonconvex multi-objective optimization problems were introduced with data uncertainty. Then, with the robust optimization approach, the robust counterpart model for the uncertain multi-objective optimization problem was built. Moreover, with the scalarization method and the generalized subdifferential properties, the optimality conditions were characterized for robust quasi approximate efficient solutions to the uncertain multi-objective optimization problem. The work generalizes and improves some results in the recent literatures.
- multi-objective optimization problem,
- quasi efficient solution,
- robust optimality condition

FullText(HTML)

References(16)

References

[1]	LUC D T. Theory of Vector Optimization [M]. Berlin: Springer-Verlag, 1989.
[2]	BOT R I, GRAD S M, WANKA G. Duality in Vector Optimization [M]. Berlin: Springer-Verlag, 2009.
[3]	彭再云, 李科科, 张石生. D-η-E- 半预不变凸映射与向量优化[J]. 应用数学和力学, 2014,35(9): 1020-1032.(PENG Zaiyun, LI Keke, ZHANG Shisheng. D-η-E -semipreinvex vector mappings and vector optimization[J]. Applied Mathematics and Mechanics,2014,35(9): 1020-1032.(in Chinese))
[4]	赵勇, 彭再云, 张石生. 向量优化问题有效点集的稳定性[J]. 应用数学和力学, 2013,34(6): 643-650.(ZHAO Yong, PENG Zaiyun, ZHANG Shisheng. Stability of the sets of effective points of vector valued optimization problems[J]. Applied Mathematics and Mechanics,2013,〖STHZ〗 34(6): 643-650.(in Chinese))
[5]	陈望, 周志昂．基于改进集的带约束集值向量均衡问题的最优性条件[J]. 应用数学和力学, 2018,39(10): 1189-1197.(CHEN Wang, ZHOU Zhiang. Optimality conditions for set-valued vector equilibrium problems with constraints involving improvement sets[J]. Applied Mathematics and Mechanics,2018,39(10): 1189-1197.(in Chinese))
[6]	BEN-TAL A, GHAOUI L E, NEMIROVSKI A. Robust Optimization [M]. Princeton: Princeton University Press, 2009.
[7]	LEE G M, LEE J H. On nonsmooth optimality theorems for robust multiobjective optimization problems[J]. Journal of Nonlinear and Convex Analysis,2015,16(10): 2039-2052.
[8]	EHRGOTT M, IDE J, SCHBEL A. Minmax robustness for multi-objective optimization problems[J]. European Journal of Operational Research,2014,239(1): 17-31.
[9]	SUN X K, PENG Z Y, GUO X L. Some characterizations of robust optimal solutions for uncertain convex optimization problems[J]. Optimization Letters,2016,10(7): 1463-1478.
[10]	FAKHAR M, MAHYARINIA M R, 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.
[11]	LORIDAN P. ε-solutions in vector minimization problems[J]. Journal of Optimization Theory and Application,1984,43(2): 265-276.
[12]	SON T Q, STRODIOT J J, NGUYEN V H. ε-optimality and ε-Lagrangian duality for a nonconvex programming problem with an infinite number of constraints[J]. Journal of Optimization Theory and Application,2009,141(2): 389-409.
[13]	SON T Q, KIM D S. ε-mixed type duality for nonconvex multiobjective programs with an infinite number of constraints[J]. Journal of Global Optimization,2013,57(2): 447-465.
[14]	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.
[15]	CLARKE F H. Optimization and Nonsmooth Analysis [M]. New York: John Wiley & Sons, 1983.
[16]	MIFFLIN R. Semismooth and semiconvex functions in constrained optimization[J]. SIAM Journal on Control and Optimization,1977,15(6): 959-972.