Characterizations of robust ε-quasi optimal solutions for nonsmooth optimization problems with uncertain data

ABSTRACT

This paper deals with robust ε-quasi optimal solutions for a class of nonsmooth optimization problems with uncertain data. Under some mild assumptions, we first establish, by using robust optimization (i.e. worst-case) approach, approximate optimality conditions for this uncertain nonsmooth optimization problem. Then, we introduce a Mixed-type robust approximate dual problem of this uncertain optimization problem, and explore their relationships. Moreover, using a scalarization method, we derive optimality conditions for robust weakly approximate efficient solutions for an uncertain nonsmooth multiobjective optimization problem. We also obtain approximate duality theorems for the uncertain nonsmooth multiobjective optimization problem.

Keywords:

• Approximate solutions
• generalized subdifferential
• robust nonsmooth optimization

2000 Mathematics Subject Classifications:

• 90C26
• 90C29
• 90C46

Acknowledgments

We would like to express our sincere thanks to the three anonymous referees for their constructive suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the Natural Science Foundation of Chongqing [grant numbers cstc2020jcyj-msxmX0016,cstc2018jcyjAX0119], the ARC Discovery Grant [grant number DP190103361], the Open Research Platform of CTBU [grant number KFJJ2019097], the Education Committee Project Foundation of Chongqing for Bayu Young Scholar, the Science and Technology Research Program of Chongqing Municipal Education Commission [grant number KJZDK201900801] and the Project of CTBU [grant number ZDPTTD201908].