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.
A Decomposition Algorithm for Two-Stage Stochastic Programs with Nonconvex Recourse
17.01.2022 15:30 - 16:30
Organiser:
R. I. Boț (University of Vienna), S. Sabach (Technion - Israel Institute of Technology Haifa), M. Staudigl (Maastricht University)
Location:
Zoom Meeting
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