报告地点：行健楼学术活动室526

邀请人：蔡邢菊教授

报告摘要：We tackle the challenging problem of stochastic weakly convex optimization subject to mixed (equality and inequality) expected-value constraints. While optimal $\mathcal{O}(\epsilon^{-3})$ sample complexity algorithms exist for unconstrained weakly convex problems, dealing with complex functional constraints typically requires cumbersome multi-loop penalty or augmented Lagrangian methods, which suffer from high inner-loop complexity and sensitive parameter tuning. To bridge this fundamental gap, we propose the primal-dual Halpern-PAGE (PD-HP) algorithm. As a purely single-loop method, PD-HP completely bypasses the computational burden of nested iterations. At each step, it merely requires solving a simple strongly convex surrogate subproblem alongside a straightforward dual projection, making it exceptionally efficient and convenient to implement. Crucially, we prove that this computationally lightweight algorithm achieves the optimal $\mathcal{O}(\epsilon^{-3})$ sample complexity for mixed-constrained stochastic weakly convex problems, successfully matching the theoretical lower bounds. Furthermore, when the primal domain is a compact polyhedral convex set, we establish the deterministic stability of the dual multipliers by exploiting the generalized Mangasarian-Fromovitz constraint qualification (MFCQ) alongside Hoffman's error bound. This ensures that our optimal complexity bound holds strictly under the standard, unbounded KKT residual metric without any theoretical gaps or artificial residual truncations.

报告人简介：

张立卫，东北大学智能工业与系统优化国家级前沿科学研究中心教授。 他于1989年，1992年，1998年分别在大连理工大学获得理学学士，硕士，博士学位，1999-2001在中科院计算数学所从事博士后工作。目前的研究兴趣是“矩阵优化”，“随机规划”和“均衡优化”。他目前主持一项国家重点研发计划课题，完成和主持自然科学基金面上基金多项,重点基金子课题两项。在国际顶级期刊Mathematical Programming, Operations Research, SIAM Journal on Optimization, Mathematics of Operations Research, Mathematics of Computation, JMLR, IEEE Transactions on Automatic Control 发表论文二十余篇。曾任中国运筹学会数学规划分会副理事长，中国运筹学会常务理事，中国运筹学会金融工程与金融风险管理分会副理事长。 现任中国运筹学会监事,《JAPOR》,《NACO》和《运筹学学报》编委，2020年获得中国运筹学会运筹研究奖。