论文标题
两阶段随机程序的分解算法，具有非convex的诉讼
A Decomposition Algorithm for Two-Stage Stochastic Programs with Nonconvex Recourse
论文作者
论文摘要
在本文中，我们研究了一种分解方法，用于求解一类非convex两阶段随机程序，其中第二阶段问题的目的和约束都是由第一阶段变量非线性参数化的。由于产生的非凸道功能的CLARKE规律性失败，因此无法将经典分解方法（例如Benders分解和（增强）基于Lagrangian的算法（增强）算法直接推广以解决此类模型。通过探索辅助功能的隐式凸孔结构，我们引入了一个基于所谓的部分莫罗封装的新型分解框架。该算法基于第二阶段凸子问题的解决方案，连续生成了辅助功能的强烈凸二次近似，并将它们添加到第一阶段的主问题中。在固定方案和内部采样均建立了收敛。进行数值实验以证明所提出算法的有效性。
In this paper, we have studied a decomposition method for solving a class of nonconvex 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 decomposition framework based on the so-called partial Moreau envelope. The algorithm successively generates strongly convex quadratic approximations of the recourse function based on the solutions of the second-stage convex subproblems and adds them to the first-stage master problem. Convergence under both fixed scenarios and interior samplings is established. Numerical experiments are conducted to demonstrate the effectiveness of the proposed algorithm.
