汇报标题 (Title)：Efficiency of Smooth Approximation Methods for Weakly Convex Optimization（求解弱凸优化的光滑近似算法的有效性）
汇报人 (Speaker)：邓琪 副教授（上海交通大学）
汇报功夫 (Time)：2025年12月11日（周四）10：30
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：周安娃
主办部门：理学院数学系
汇报提要： Standard complexity analyses for weakly convex optimization rely on the Moreau envelope technique proposed by Davis and Drusvyatskiy (2019). The main insight is that nonsmooth algorithms, such as proximal subgradient, proximal point, and their stochastic variants, implicitly minimize a smooth surrogate function induced by the Moreau envelope. Meanwhile, explicit smoothing, which directly minimizes a smooth approximation of the objective, has long been recognized as an efficient strategy for nonsmooth optimization. In this paper, we generalize the notion of smoothable functions, originally introduced by Nesterov (2005) and later expanded by Beck and Teboulle (2012) for nonsmooth convex optimization. This generalization provides a unified viewpoint on several important smoothing techniques for weakly convex optimization, including Nesterov-type smoothing and Moreau envelope smoothing. Our theory yields a framework for designing smooth approximation algorithms for both deterministic and stochastic weakly convex problems with provable complexity guarantees. Furthermore, our theory extends to the smooth approximation of non-Lipschitz functions, allowing for complexity analysis even when global Lipschitz continuity does not hold.
