题 目：Algorithmic Development for Computing D-Stationary Points of a Class of Nonsmooth DC Minimization
报 告 人：周子锐 助理教授 (邀请人：李董辉)
时 间：2019-07-09 16:00--17：00
周子锐，香港浸会大学数学系助理教授，2015年于香港中文大学获得系统工程与工程管理博士学位。2016至2018年度，在西蒙弗雷泽大学数学和统计系从事博士后研究。他的主要研究方向为连续优化的理论和算法，及其在机器学习和信号处理等领域的应用。至今已在SIAM Journal on Optimization和Mathmetical Programming优化国际顶级期刊上发表数篇论文。
In this talk we study numerical solutions for a class of structured nonsmooth difference-of-convex (DC) minimization in which the first convex component is the sum of a smooth and a nonsmooth function while the second convex component is the supremum of finitely many convex smooth functions. The existing methods for this problem usually have weak convergence guarantee or exhibit slow convergence. Due to this, we propose two nonmonotone enhanced proximal DC algorithms for solving this problem. For possible
acceleration, one uses a nonmonotone line search scheme in which the associated Lipschitz constant is adaptively approximated by some local curvature information of the smooth function in the first convex component, and the other employs an extrapolation scheme. We show that every accumulation point of the solution sequence generated by them is a D-stationary point of the problem. These methods may, however, become inefficient when the number of convex smooth functions in defining the second convex component is large. To remedy this issue, we propose randomized counterparts for them and show that every accumulation point of the generated solution sequence is a D-stationary point of the problem almost surely. We shall also present some preliminary numerical experiments to demonstrate the efficiency of the proposed algorithms.