STABILITY ANALYSIS OF OPTIMIZATION PROBLEMS WITH kTH ORDER STOCHASTIC AND DISTRIBUTIONALLY ROBUST DOMINANCE CONSTRAINTS INDUCED BY FULL RANDOM

In this paper, we consider stochastic optimization problems with kth order dominance constraints induced by full random recourse. We first introduce the optimization model with dominance constraints and its distributionally robust counterpart. After establishing the closedness and convexity of the feasible solution set, we derive the qualitative stability about the constraint set mapping with respect to the simultaneous perturbations of the random variable and the benchmark. Furthermore, we obtain the quantitative stability results of the constraint set mapping, the optimal value function and the optimal solution set under the Hausdorff metric, which extend the present results to the locally Lipschitz continuity case. Finally, for stochastic optimization problems with kth order distributionally robust dominance constraints, we derive the corresponding quantitative stability results under the appropriate pseudometric.