2020/04/05 by Xiaopeng Luo, Xin Xu, Luo, Xiaopeng +3
Computer Science · Engineering · Mathematics · #65K05 #68Q25 #90C26 #90C56 #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2004.02210
openalex publication_date 2020/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose and analyze asymptotic proximal point (APP) methods to find the global minimizer for a class of nonconvex, nonsmooth, or even discontinuous multiple minima functions. The method is based on an asymptotic representation of nonconvex proximal points so that it can find the global minimizer without being trapped in saddle points, local minima, or even discontinuities. Our main result shows that the method enjoys the global linear convergence for such a class of functions. Furthermore, the method is derivative-free and its per-iteration cost, i.e., the number of function evaluations, is also bounded, so it has a complexity bound O(log\frac1ε) for finding a point such that the gap between this point and the global minimizer is less than ε>0. Numerical experiments and comparisons in various dimensions from 2 to 500 demonstrate the benefits of the method.