11 papers · 1 filter
Global Linear Convergence of the Proximal Bundle Method under Unknown Piecewise Smoothness and Quadratic Growth
Zhenwei Lin, Zhe Zhang
We study why the proximal bundle method (PBM) can perform better in practice when it retains more cutting planes. We consider convex objectives with quadratic growth and an unknown…
A Technical Note on the Implementation and Use of PDCS
Zhenwei Lin, Zikai Xiong, Dongdong Ge +1
This technical note documents the implementation and use of the Primal-Dual Conic Programming Solver (PDCS), a first-order solver for large-scale conic optimization problems introd…
Accelerated Prox-Level Methods for Unknown Piecewise-Smooth Optimization I: Convex Optimization
Zhenwei Lin, Zhe Zhang
We introduce a nearly parameter-free algorithm for minimizing piecewise smooth (PWS) convex functions under the quadratic-growth (QG) condition, where the locations and structure o…
Revisiting Randomized Smoothing: Nonsmooth Nonconvex Optimization Beyond Global Lipschitz Continuity
Jingfan Xia, Zhenwei Lin, Qi Deng
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a…
A Practical GPU-Enhanced Matrix-Free Primal-Dual Method for Large-Scale Conic Programs
Zhenwei Lin, Zikai Xiong, Dongdong Ge +1
In this paper, we introduce a practical GPU-enhanced matrix-free first-order method for solving large-scale conic programming problems, which we refer to as PDCS, standing for the…
Uniformly Optimal and Parameter-free First-order Methods for Convex and Function-constrained Optimization
Qi Deng, Guanghui Lan, Zhenwei Lin
This paper presents new first-order methods for achieving optimal oracle complexities in convex optimization with convex functional constraints. Oracle complexities are measured by…
Accelerating Low-Rank Factorization-Based Semidefinite Programming Algorithms on GPU
Qiushi Han, Zhenwei Lin, Hanwen Liu +4
In this paper, we address a long-standing challenge: how to achieve both efficiency and scalability in solving semidefinite programming problems. We propose breakthrough accelerati…
A Single-Loop Robust Policy Gradient Method for Robust Markov Decision Processes
Zhenwei Lin, Chenyu Xue, Qi Deng +1
Robust Markov Decision Processes (RMDPs) have recently been recognized as a valuable and promising approach to discovering a policy with creditable performance, particularly in the…
A Low-Rank ADMM Splitting Approach for Semidefinite Programming
Qiushi Han, Chenxi Li, Zhenwei Lin +5
We introduce a new first-order method for solving general semidefinite programming problems, based on the alternating direction method of multipliers (ADMM) and a matrix-splitting…
Decentralized Gradient-Free Methods for Stochastic Non-Smooth Non-Convex Optimization
Zhenwei Lin, Jingfan Xia, Qi Deng +1
We consider decentralized gradient-free optimization of minimizing Lipschitz continuous functions that satisfy neither smoothness nor convexity assumption. We propose two novel gra…
Faster Accelerated First-order Methods for Convex Optimization with Strongly Convex Function Constraints
Zhenwei Lin, Qi Deng
In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best…