8 papers
Halpern-Accelerated Majorized ADMM with Optimal Non-Ergodic Convergence under Degenerate Preconditioning
Ning Zhang, Benqi Liu, Liwei Zhang
We develop a Halpern-accelerated majorized alternating direction method of multipliers (ADMM) with possibly indefinite proximal terms for linearly constrained convex composite opti…
A counterexample to global convergence of classical DFP under the standard strong Wolfe conditions
Benqi Liu, Zichen Wang, Zaiwen Wen +2
A long-standing open question in quasi-Newton optimization asks whether the classical Davidon--Fletcher--Powell (DFP) method converges globally on uniformly convex objectives when…
A Quadratic-Approximation-Based Stochastic Approximation Method for Weakly Convex Stochastic Programming
Yule Zhang, Benqi Liu, Xiantao Xiao +1
We propose a novel stochastic approximation algorithm, termed PMQSopt, for solving weakly convex stochastic optimization problems involving expectation-valued functions. The algori…
A Proximal Augmented Lagrangian Method Based on Quadratic Approximations for Weakly Convex Optimization
Yule Zhang, Benqi Liu, Xiantao Xiao +1
This paper proposes QPALM, a proximal augmented Lagrangian method based on quadratic approximations, for solving nonlinear programming problems with weakly convex objective and con…
Push-Pull Based Distributed Primal-Dual Algorithm for Coupled Constrained Convex Optimization in Multi-Agent Networks
Kai Gong, Liwei Zhang
This paper focuses on a distributed coupled constrained convex optimization problem over directed unbalanced and time-varying multi-agent networks, where the global objective funct…
Augmented Lagrangian Methods for Time-varying Constrained Online Convex Optimization
Haoyang Liu, Xiantao Xiao, Liwei Zhang
In this paper, we consider online convex optimization (OCO) with time-varying loss and constraint functions. Specifically, the decision maker chooses sequential decisions based onl…
Regrets of Proximal Method of Multipliers for Online Non-convex Optimization with Long Term Constraints
Liwei Zhang, Haoyang Liu, Xiantao Xiao
The online optimization problem with non-convex loss functions over a closed convex set, coupled with a set of inequality (possibly non-convex) constraints is a challenging online…
Solving Stochastic Optimization with Expectation Constraints Efficiently by a Stochastic Augmented Lagrangian-Type Algorithm
Liwei Zhang, Yule Zhang, Jia Wu +1
This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximati…