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  1. Free, publicly-accessible full text available June 1, 2026
  2. In this paper, we have studied a decomposition method for solving a class of non-convex two-stage stochastic programs, where both the objective and constraints of the second-stageproblem are nonlinearly parameterized by the first-stage variables. Due to the failure of the Clarkeregularity of the resulting nonconvex recourse function, classical decomposition approaches such asBenders decomposition and (augmented) Lagrangian-based algorithms cannot be directly generalizedto 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. Thealgorithm successively generates strongly convex quadratic approximations of the recourse functionbased on the solutions of the second-stage convex subproblems and adds them to the first-stage mas-ter problem. Convergence has been established for both a fixed number of scenarios and a sequentialinternal sampling strategy. Numerical experiments are conducted to demonstrate the effectiveness of the proposed algorithm. 
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