7 papers
Weak Convexity and Proximal Bundle Methods for Nonsmooth Policy Optimization in Robust Control
Yuto Watanabe, Feng-Yi Liao, Yang Zheng
We study policy optimization for discrete-time robust control with static output-feedback, and present the first feasibility-preserving algorithm with a determ…
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…
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…
Inexact Augmented Lagrangian Methods for Conic Programs: Quadratic Growth and Linear Convergence
Feng-Yi Liao, Lijun Ding, Yang Zheng
Augmented Lagrangian Methods (ALMs) are widely employed in solving constrained optimizations, and some efficient solvers are developed based on this framework. Under the quadratic…
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…