A Proximal-Type Method for Nonsmooth and Nonconvex Constrained Minimization Problems
提出一种可实现的近端型方法，处理非光滑非凸目标和约束函数，通过有限个凸模型逐点最小构造非凸模型，计算满足模型临界性条件的点，数值实验验证了有效性。
Abstract This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model approximating the nonconvex functions, our approach can work with a nonconvex model constructed by the pointwise minimum of finitely many convex models. The latter can be chosen with reasonable flexibility to better fit the underlying functions’ structure. We provide a unifying framework and analysis covering several subclasses of composite optimization problems and show that our method computes points satisfying certain necessary optimality conditions, which we will call model criticality. Depending on the specific model being used, our general concept of criticality boils down to standard necessary optimality conditions. Numerical experiments on some stochastic reliability-based optimization problems illustrate the practical performance of the method.