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

This paper deals with robust epsilon-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.

Automated summary

This paper discusses robust epsilon-quasi optimal solutions for nonsmooth optimization problems with uncertain data, establishing approximate optimality conditions and exploring relationships through robust optimization and a mixed-type robust approximate dual problem. Optimal conditions for robust weakly approximate efficient solutions for an uncertain nonsmooth multiobjective optimization problem are derived using a scalarization method, along with approximate duality theorems for the problem.