7 papers
An accelerated proximal bundle method for convex optimization
Feng-Yi Liao, Thomas Madden, Yang Zheng
The proximal bundle method (PBM) is a powerful and widely used approach for minimizing nonsmooth convex functions. However, for smooth objectives, its best-known convergence rate r…
Error bounds, PL condition, and quadratic growth for weakly convex functions, and linear convergences of proximal point methods
Feng-Yi Liao, Lijun Ding, Yang Zheng
Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weake…
An Overview and Comparison of Spectral Bundle Methods for Primal and Dual Semidefinite Programs
Feng-Yi Liao, Lijun Ding, Yang Zheng
The spectral bundle method developed by Helmberg and Rendl is well-established for solving large-scale semidefinite programs (SDPs) in the dual form, especially when the SDPs admit…
Policy Optimization in Robust Control: Weak Convexity and Subgradient Methods
Yuto Watanabe, Feng-Yi Liao, Yang Zheng
Robust control seeks stabilizing policies that perform reliably under adversarial disturbances, with control as a classical formulation. It is known that polic…
A Proximal Descent Method for Minimizing Weakly Convex Optimization
Feng-Yi Liao, Yang Zheng
We study the problem of minimizing a -weakly convex and possibly nonsmooth function. Weak convexity provides a broad framework that subsumes convex, smooth, and many composite n…
A Bundle-based Augmented Lagrangian Framework: Algorithm, Convergence, and Primal-dual Principles
Feng-Yi Liao, Yang Zheng
We propose a new bundle-based augmented Lagrangian framework for solving constrained convex problems. Unlike the classical (inexact) augmented Lagrangian method (ALM) that has a ne…