Hybrid Algorithms for Finding a D-Stationary Point of a Class of Structured Nonsmooth DC Minimization
针对一类结构化非光滑DC最小化问题，提出混合算法先计算近似临界点再检查是否为近似D-稳定点，证明了子序列收敛性，数值实验验证了效率。
.In this paper, we consider 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 guarantees or need to solve lots of subproblems per iteration. Due to this, we propose hybrid algorithms for solving this problem in which we first compute approximate critical points and then check whether these points are approximate D-stationary points. Under suitable conditions, we prove that there exists a subsequence of iterates of which every accumulation point is a D-stationary point. Some preliminary numerical experiments are conducted to demonstrate the efficiency of the proposed algorithms.Keywordsnonsmooth DC programD-stationary pointDCAMSC codes90C2690C3065K05