报告题目 (Title)：A stochastic primal-dual method for a class of nonconvex constrained optimization(一类非凸约束优化问题的随机原始-对偶算法)
报告人 (Speaker)： 王晓 副研究员（深圳鹏城国家重点实验室）
报告时间 (Time)：2021年11月18日(周四) 10:00
报告地点 (Place)：腾讯会议：424 169 964
邀请人(Inviter)：徐姿
主办部门：理学院数学系
报告摘要：We study a class of nonconvex optimization which involves uncertainty in the objective and a large number of nonconvex functional constraints. Challenges often arise when solving this type of problems due to the nonconvexity of the feasible set and the high cost of simultaneously calculating function value and gradient of all constraints. To handle these issues, we propose a stochastic primal-dual method in this paper. At each iteration, a proximal subproblem based on a stochastic approximation to an augmented Lagrangian function is solved to update primal variables, whose latest information is further used to update dual variables. We then explore theoretical properties of the proposed algorithm and establish the $\tilde{O}(\epsilon^{-4})$ iteration complexity to find an $\epsilon$-stationary point of the original problem. Numerical tests on a weighted maximin dispersion problem and a nonconvex quadratically constrained optimization problem demonstrate the promising performance of the proposed algorithm.
