Continuity and stability of fully random two-stage stochastic programs with mixed-integer recourse

In order to derive continuity and stability of two‐stage stochastic programs with mixed‐integer recourse when all coefficients in the second‐stage problem are random, we first investigate the quantitative continuity of the objective function of the corresponding continuous recourse problem with random recourse matrices. Then by extending derived results to the mixed‐integer recourse case, the perturbation estimate and the piece‐wise lower semi‐continuity of the objective function are proved. Under the framework of weak convergence for probability measure, the epi‐continuity and joint continuity of the objective function are established. All these results help us to prove a qualitative stability result. The obtained results extend current results to the mixed‐integer recourse with random recourse matrices which have finitely many atoms.