Perturbation analysis of a class of composite optimization problems
报告专家：唐培培（浙大城市学院）
报告时间：2024年6月20日（星期四）上午16：30-17：30
报告地点：研究生院三区204
报告摘要：In this talk, we consider the perturbation analysis of a class of composite optimization problems, which is a unified framework for developing both theoretical and algorithmic issues of constrained optimization problems. We take full advantage of the properties of the graphical derivative, regular coderivative and limiting coderivative and provide a definition of a strong second order sufficient condition (SSOSC) for the composite optimization problem, which can not be extended directly from the definitions of the known specific problems. Under some mild assumptions on the objective function, we prove that the following conditions are equivalent to each other: the SSOSC and the nondegeneracy condition, the nonsingularity of Clarke’s generalized Jacobian of the nonsmooth system at a Karush-Kuhn-Tucker (KKT) point, and the strong regularity of the KKT point. These results provide an important way to characterize the stability of the KKT point. As for the convex composite optimization problem, which is a special case of the general problem, we establish the equivalence between the primal/dual second order sufficient condition and the dual/primal strict Robinson constraint qualification, the equivalence between the primal/dual SSOSC and the dual/primal nondegeneracy condition. Moreover, we prove that the dual nondegeneracy condition and the nonsingularity of Clarke’s generalized Jacobian of the subproblem corresponding to the augmented Lagrangian method are also equivalent to each other. These theoretical results lay solid foundation for designing an efficient algorithm.
专家简介：唐培培，浙大城市学院计算机与计算科学学院副教授，2009年获浙江大学计算数学博士学位。主要致力于机器学习中大规模非光滑优化问题的理论、算法研究，在《Journal of Machine Learning Research》、《IEEE Transactions on Signal Processing》、《Computational Optimization and Applications》等杂志发表了多篇文章，入选杭州市“131”人才，承担参与多项省部级课题。
邀请人：宋恩彬
