On robustness for set-valued optimization problems

Abstract

Robust optimization is an important subfield of optimization that deals with uncertainty in the data of optimization problems. Consider the robust set-valued optimization problem min F (x, ξ) subject to x ∈ X, (RSOP ) where F : X × U ⇒ Y is a set-valued map, where U ⊆ Rk is the set of uncertainty. we define a set-valued map FU : X ⇒ Y as FU (x) = [ ξ∈U F (x, ξ). We consider the following set-valued robust counterpart to (RSOP): min FU (x) subject to x ∈ X. (SOP ) In this paper, we study the existence robust efficient solution for robust set- valued optimization problem with unbounded feasible sets by noncoercivity condition via asymptotic analytic tools.