The MAEG-R method achieves convergence for monotone inclusions with merely continuous operators via a moving-anchor restart strategy, while preserving O(1/k) complexity in the Lipschitz case.
Hpr-qp: A dual halpern peaceman-rachford method for solving large-scale convex composite quadratic programming
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abstract
In this paper, we introduce HPR-QP, a dual Halpern Peaceman-Rachford (HPR) method designed for solving large-scale convex composite quadratic programming. One distinctive feature of HPR-QP is that, instead of working with the primal formulations, it builds on the novel restricted Wolfe dual introduced in recent years. It also leverages the symmetric Gauss-Seidel technique to simplify subproblem updates without introducing auxiliary slack variables that typically lead to slow convergence. By restricting updates to the range space of the Hessian of the quadratic objective function, HPR-QP employs proximal operators of smaller spectral norms to speed up the convergence. Shadow sequences are elaborately constructed to deal with the range space constraints. Additionally, HPR-QP incorporates adaptive restart and penalty parameter update strategies, derived from the HPR method's $O(1/k)$ convergence in terms of the Karush-Kuhn-Tucker residual, to further enhance its performance and robustness. Extensive numerical experiments on benchmark data sets using a GPU demonstrate that our Julia implementation of HPR-QP significantly outperforms state-of-the-art solvers in both speed and scalability.
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math.OC 4years
2026 4roles
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use method 1representative citing papers
An efficiently computable HS-Jacobian acts as a conservative mapping for projections onto polyhedral sets, supporting provably convergent Adam-based end-to-end training of linearly constrained deep neural networks.
DSPDHG extends PDHG and SPDHG with doubly stochastic block updates and proves O(1/K) ergodic convergence for the expected restricted primal-dual gap plus linear convergence for a restarted variant under quadratic growth.
Develops restarted accelerated primal-dual methods with monotone and non-monotone adaptive stepsizes that achieve global linear convergence for nonlinear conic convex programs under metric subregularity of the KKT mapping.
citing papers explorer
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Convergence Analysis of the Restarted Moving-Anchored Extra-Gradient Method in the Absence of Local Lipschitz Continuity
The MAEG-R method achieves convergence for monotone inclusions with merely continuous operators via a moving-anchor restart strategy, while preserving O(1/k) complexity in the Lipschitz case.
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Efficient and provably convergent end-to-end training of deep neural networks with linear constraints
An efficiently computable HS-Jacobian acts as a conservative mapping for projections onto polyhedral sets, supporting provably convergent Adam-based end-to-end training of linearly constrained deep neural networks.
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On the convergence of doubly stochastic Primal-Dual Hybrid Gradient Method
DSPDHG extends PDHG and SPDHG with doubly stochastic block updates and proves O(1/K) ergodic convergence for the expected restricted primal-dual gap plus linear convergence for a restarted variant under quadratic growth.
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Restarted Accelerated Primal-Dual Algorithms with Adaptive Stepsizes for Nonlinear Conic Constrained Convex Optimization
Develops restarted accelerated primal-dual methods with monotone and non-monotone adaptive stepsizes that achieve global linear convergence for nonlinear conic convex programs under metric subregularity of the KKT mapping.