HUANet is a deep neural network architecture that unrolls the Alternating Direction Method of Multipliers (ADMM) into a trainable model for accelerating parametric constrained convex optimization. It embeds a hard‑constrained neural network in each ADMM iteration, using a differentiable correction stage to enforce affine equalities of the primal subproblem. The method also incorporates first‑order optimality conditions into a self‑supervised training loss, and numerical experiments on benchmark problems and a control application demonstrate its effectiveness in speeding up constrained convex optimization.
By Trinh Tran, Binh Nguyen, Truong X. Nghiem
arXiv:2508. 00775v2 Announce Type: replace-cross Abstract: The design of many classical optimization algorithms is driven by the certification of linear convergence rates over classes of optimization problems.
By Andrea Martin, Ian R. Manchester, Luca Furieri
arXiv:2601. 16510v3 Announce Type: replace-cross Abstract: Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost.
By Liping Tao, Xindi Tong, Chee Wei Tan
arXiv:2209. 03282v5 Announce Type: replace-cross Abstract: Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research.
By John Chiang
arXiv:2610.02182v1 Announce Type: cross
Abstract: Quasi-Newton (QN) methods have long been among the most effective methods for large-scale unconstrained convex optimization. Two obstacles have limit...
By Joohwan Ko, Tetiana Parshakova, Diana Cai, Robert M. Gower
arXiv:2608. 09523v1 Announce Type: new Abstract: Deep neural network (DNN) training with stochastic gradient descent (SGD) and its variants achieves strong empirical performance, yet classical optimization theory does not fully explain this success.
By Binchuan Qi
arXiv:2409. 08066v3 Announce Type: replace Abstract: The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control.
By Lukas L\"uken, Sergio Lucia
arXiv:2412. 19444v2 Announce Type: replace Abstract: Optimization algorithms such as AdaGrad and Adam have significantly advanced the training of deep models by dynamically adjusting the learning rate during the optimization process.
By Yuanzhe Tao, Yifeng Liu, Huizhuo Yuan, Xun Zhou, Yuan Cao, Quanquan Gu
arXiv:2512. 02342v3 Announce Type: replace-cross Abstract: The stochastic Polyak step size (SPS) has proven to be a promising choice for stochastic gradient descent (SGD), delivering competitive performance relative to state-of-the-art methods on smooth convex and non-convex optimization problems, including deep neural network training.
By Dimitris Oikonomou, Nicolas Loizou
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By Yicong Jiang, Feihu Huang
arXiv:2512. 02494v2 Announce Type: replace Abstract: Differentiable optimization layers enable learning systems to make decisions by solving embedded optimization problems.
By Zihao Zhao, Kai-Chia Mo, Shing-Hei Ho, Brandon Amos, Kai Wang
arXiv:2409. 03682v2 Announce Type: replace Abstract: Learning new tasks by leveraging prior experience is a fundamental trait of intelligent systems.
By El Mahdi Chayti, Martin Jaggi