5 papers
Accuracy Certificates for Convex Optimization at Accelerated Rates via Primal-Dual Averaging
Matthew X. Burns, Jiaming Liang
Many works in convex optimization provide rates for achieving a small primal gap. However, this quantity is typically unavailable in practice. In this work, we show that solving a…
Multi-cut stochastic approximation methods for solving stochastic convex composite optimization
Jiaming Liang, Renato D. C. Monteiro, Honghao Zhang
This paper considers the stochastic convex composite optimization problem and presents multi-cut stochastic approximation (SA) methods for solving it, whose models in expectation o…
Improved Analysis of Restarted Accelerated Gradient and Augmented Lagrangian Methods via Inexact Proximal Point Frameworks
Matthew X. Burns, Jiaming Liang
This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradi…
Universal subgradient and proximal bundle methods for convex and strongly convex hybrid composite optimization
Vincent Guigues, Jiaming Liang, Renato D. C. Monteiro
This paper develops two parameter-free methods for solving convex and strongly convex hybrid composite optimization problems, namely, a composite subgradient type method and a prox…
Primal-dual proximal bundle and conditional gradient methods for convex problems
Jiaming Liang
This paper studies the primal-dual convergence and iteration-complexity of proximal bundle methods for solving nonsmooth problems with convex structures. More specifically, we deve…