A Decomposition Framework for Nonlinear Nonconvex Two-Stage Optimization
提出一种新的分解框架，处理两阶段都非凸的连续约束优化问题。通过内点平滑技术让第二阶段最优解对第一阶段参数可微，从而直接使用现成优化求解器，并证明能收敛到一阶最优点。适合求解大规模实例。
Abstract. We propose a new decomposition framework for continuous nonlinear constrained two-stage optimization, where both first- and second-stage problems can be nonconvex. A smoothing technique based on an interior-point formulation renders the optimal solution of the second-stage problem differentiable with respect to the first-stage parameters. As a consequence, efficient off-the-shelf optimization packages can be utilized. We show that the solution of the nonconvex second-stage problem behaves locally like a differentiable function so that existing proofs can be applied to prove the convergence of the iterates to first-order optimal points for the first stage. We also prove fast local convergence of the algorithm as the barrier parameter is driven to zero. Numerical experiments for large-scale instances demonstrate the computational advantages of the decomposition framework.