A Decomposition Algorithm for Two-Stage Stochastic Programs with Nonconvex Recourse Functions

Publication Date: March 31, 2024

Li, Hanyang & Cui, Ying. (2024). A Decomposition Algorithm for Two-Stage Stochastic Programs with Nonconvex Recourse Functions. SIAM Journal on Optimization. 34. 306-335. 10.1137/22M1488533.


In this paper, we have studied a decomposition method for solving a class of nonconvex two-stage stochastic programs, where both the objective and constraints of the second-stage problem are nonlinearly parameterized by the first-stage variables. Due to the failure of the Clarke regularity of the resulting nonconvex recourse function, classical decomposition approaches such as Benders decomposition and (augmented) Lagrangian-based algorithms cannot be directly generalized to solve such models. By exploring an implicitly convex-concave structure of the recourse function, we introduce a novel decomposition framework based on the so-called partial Moreau envelope. The algorithm successively generates strongly convex quadratic approximations of the recourse function based on the solutions of the second-stage convex subproblems and adds them to the first-stage master problem.