##### Department of Mathematics,

University of California San Diego

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### Math 278C - Optimization and Data Science

## Ying Cui

#### University of Minnesota

## A decomposition algorithm for two-stage stochastic programs with nonconvex recourse

##### 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.

Host: Jiawang Nie

### February 16, 2022

### 3:00 PM

https://ucsd.zoom.us/j/94927846567

Meeting ID: 949 2784 6567

Password: 278CWN22

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