Efficiency Optimality Conditions for Convex Adjustable Robust Multiobjective Optimizations and Applications

In this paper, we consider a class of adjustable robust multiobjective optimization problem (ARMP) with convex data. We first give a non-adjustable robust form of ARMP that includes fully robust constraints and does not require any uncertainty set structure. Karush–Kuhn–Tucker conditions for weakly robust efficient, robust efficient, and Geoffrion's proper robust efficient solutions are obtained under specific constraint qualifications or qualification conditions. As an application, the linear adjustable robust optimization problem is examined. These results become simpler and have the potential for tractability analysis. Some examples are provided for analyzing and illustrating the obtained results.