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…
The Minimum Q-Order of BFGS with Exact Line Search Is One
Benqi Liu, Chenyi Li, Zaiwen Wen
Powell asked whether the smoothness assumptions underlying classical superlinear convergence force a fixed power law between adjacent iterates of exact-line-search variable-metric…
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 Fixed-Penalty Linearized Augmented Lagrangian Method with Classical Multiplier Updates
Benqi Liu, Kangkang Deng, Zichen Wang +1
Augmented Lagrangian methods are effective for nonlinear equality-constrained optimization, but solving their nonlinear primal subproblems can be expensive. For smooth nonconvex pr…
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…
Restarted Reflected Halpern Acceleration for Augmented Primal-Dual Methods
Benqi Liu, Ju Cao, Wotao Yin +1
We study linearly constrained composite convex optimization with a smooth term and a proximable nonsmooth term. We develop a unified augmented primal-dual framework with primal-dua…
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…
An explicit decomposition of higher Deligne-Lsuztig representations
Ben Liu, Sian Nie
In a previous paper, the second named author obtains a decomposition of an elliptic higher Deligne-Lusztig representation into irreducible summands, which are built in the same way…