Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications

This article is devoted to investigate a nonsmooth/nonconvex uncertain multiobjective optimization problem with composition fields (\((\text {CUP})\) for brevity) over arbitrary Asplund spaces. Employing some advanced techniques of variational analysis and generalized differentiation, we establish necessary optimality conditions for weakly robust efficient solutions of \((\text {CUP})\) in terms of the limiting subdifferential. Sufficient conditions for the existence of (weakly) robust efficient solutions to such a problem are also driven under the new concept of pseudo-quasi convexity for composite functions. We formulate a Mond–Weir-type robust dual problem to the primal problem \((\text {CUP})\), and explore weak, strong, and converse duality properties. In addition, the obtained results are applied to an approximate uncertain multiobjective problem and a composite uncertain multiobjective problem with linear operators.