题  目: Stochastic nested primal-dual method for nonconvex constrained composition optimizations

主讲人: 金玲子 博士

单  位: 香港理工大学

时  间: 12月13日9:30

腾 讯 ID:  735-218-576

密  码: 1213

摘  要： In this paper we study the nonconvex constrained composition optimization, in which the objective contains a composition of two expected-value functions whose accurate information is normally expensive to calculate. We propose a STochastic nEsted Primal-dual (STEP) method for such a problems. In each iteration, with an auxiliary variable introduced to track the inner layer function values we compute stochastic gradients of the nested function using a subsampling strategy. For nonconvex constraints, we construct a stochastic approximation to the linearized augmented Lagrangian function to update the primal variable, which further motivates to update the dual variable in a weighted-average way. We analyze the KKT measure at the output by the STEP method with constant parameters and establish its iteration and sample complexities to find an e-stationary point. Numerical results on a risk-averse portfolio optimization problem and orthogonal nonnegative matrix decomposition reveal the effectiveness of the proposed algorithms.

简  介：金玲子，香港理工大学应用数学系2021级博士研究生，导师为陈小君教授。她于2019年获上海大学数学与应用数学学士学位，2022年在王晓教授指导下获中国科学院大学数学科学学院运筹学与控制论专业理学硕士学位。她的研究兴趣为非线性优化算法具体包括非凸约束优化算法和期望优化问题的随机近似算法。研究论文发表在Computational optimization and applications上。