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

17.01.2022 15:30 - 16:30

Ying Cui (University of Minnesota)

Abstract: We study the decomposition methods for solving a class of nonconvex and nonsmooth two-stage stochastic programs, where both the objective and constraints of the second-stage problem are nonlinearly parameterized by the first-stage variable. 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 surrogate decomposition framework based on the so-called partial Moreau envelope. Convergence for both fixed scenarios and interior sampling strategy is established. Numerical experiments are conducted to demonstrate the effectiveness of the proposed algorithm.

R. I. Boț (University of Vienna), S. Sabach (Technion - Israel Institute of Technology Haifa), M. Staudigl (Maastricht University)
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