5 papers · 1 filter
A Near-optimal Method for Linearly Constrained Composite Non-convex Non-smooth Problems
Wei Liu, Qihang Lin, Yangyang Xu
We study first-order methods (FOMs) for solving \emph{composite nonconvex nonsmooth} optimization with linear constraints. Recently, the lower complexity bounds of FOMs on finding…
Lower Complexity Bounds of First-order Methods for Affinely Constrained Composite Non-convex Problems
Wei Liu, Qihang Lin, Yangyang Xu
Many recent studies on first-order methods (FOMs) focus on \emph{composite non-convex non-smooth} optimization with linear and/or nonlinear function constraints. Upper (or worst-ca…
A stochastic smoothing framework for nonconvex-nonconcave minEmax problems with applications to Wasserstein distributionally robust optimization
Wei Liu, Muhammad Khan, Gabriel Mancino-Ball +1
We study a class of stochastic nonsmooth optimization problems in which an outer variable minimizes the expectation of a pointwise maximum. This minimization--expectation--maximiza…
A single-loop SPIDER-type stochastic subgradient method for expectation-constrained nonconvex nonsmooth optimization
Wei Liu, Yangyang Xu
Many real-world problems, such as those with fairness constraints, involve complex expectation constraints and large datasets, necessitating the design of efficient stochastic meth…
Damped Proximal Augmented Lagrangian Method for weakly-Convex Problems with Convex Constraints
Hari Dahal, Wei Liu, Yangyang Xu
We give a damped proximal augmented Lagrangian method (DPALM) for solving problems with a weakly-convex objective and convex linear/nonlinear constraints. Instead of taking a full…