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We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of this class is that the inner function may fail to be locally Lipschitz continuous. It covers a range of important, yet challenging, applications, including inverse optimal value optimization and problems under value-at-risk constraints. We propose an asymptotic decomposition of the composite function that guarantees epi-convergence to the original function, leading to necessary optimality conditions for the corresponding minimization problem. The proposed decomposition also enables us to design a numerical algorithm such that any accumulation point of the generated sequence, if it exists, satisfies the newly introduced optimality conditions. These results expand on the study of so-called amenable functions introduced by Poliquin and Rockafellar in 1992, which are compositions of convex functions with smooth maps, and the prox-linear methods for their minimization. To demonstrate that our algorithmic framework is practically implementable, we further present verifiable termination criteria and preliminary numerical results. Funding: Financial support from the National Science Foundation Division of Computing and Communication Foundations [Grant CCF-2416172] and Division of Mathematical Sciences [Grant DMS-2416250] and the National Cancer Institute, National Institutes of Health [Grant 1R01CA287413-01] is gratefully acknowledged. 

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.