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:2610.32598v1 Announce Type: cross
Abstract: Symmetric polyconvexity provides a sufficient condition for weak lower semicontinuity in small-strain elasticity and a tractable lower bound for the...
By Florian Gammer
arXiv:2608. 09707v1 Announce Type: cross Abstract: Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research.
By Yu Liu, Jan Kronqvist, Fabricio Oliveira
arXiv:2605.24437v2 Announce Type: replace
Abstract: We present a novel framework for embedding hard constraint satisfaction into neural network (NN) architectures, specifically feedforward neural net...
By Yang Zhao, Jungeun Lee, Jeong hwan Jeon, Sze Zheng Yong
The paper introduces a layerwise, decoupled approach to structurally sparsify fully connected layers in pretrained neural networks. By extracting shallow two‑layer subnetworks, normalizing inner weights, and applying a structured group penalty to each block’s outer weight matrix, the method prunes neurons sequentially and reduces layer widths. The authors prove equivalence to a joint penalty for positively homogeneous activations, and demonstrate that this decoupled formulation is more robust, offering a broader regularization range and lower catastrophic over‑pruning while preserving accuracy in classification, sparse‑recovery, PINN, and OPT‑1.3B experiments.
By Charles Kulick, Armenak Petrosyan, Sui Tang
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:2608.24743v1 Announce Type: new
Abstract: Existing linear program (LP) and semidefinite program (SDP) relaxations for rectified linear unit (ReLU) neural network (NN) verification yield overly-...
By Hanna Jiamei Zhang, Alan Papalia, Michael Everett, David M. Rosen
arXiv:2502. 11152v4 Announce Type: replace-cross Abstract: The optimization foundations of deep linear networks have recently received significant attention.
By Po Chen, Rujun Jiang, Peng Wang
Existing linear program (LP) and semidefinite program (SDP) relaxations for rectified linear unit (ReLU) neural network (NN) verification yield overly-conservative safety guarantees due to significant...
The paper introduces the "lift" technique for training input‑convex neural networks, replacing the traditional non‑negative weight constraint enforced by projected gradient descent or a softplus map. By adding a learnable slack variable and an unconstrained network that processes a permutation‑invariant batch summary, the lift couples batch‑dependent latent weights to the gradient, increasing update variance and enabling faster escape from the softplus shoulder. Experiments show that when the softplus method stalls at the shoulder, the lift achieves tighter fits and reconstructs targets roughly three times faster, while both methods agree when the shoulder is rarely reached.
By Ali Siahkoohi
arXiv:2608.09523v2 Announce Type: replace
Abstract: Stochastic gradient descent (SGD) and its variants train deep neural networks (DNNs) effectively in practice, yet classical optimization theory doe...
By Binchuan Qi
Convex‑SKM‑Net is a neural layer that enforces convex constraints by constructing linearization halfspaces from residual and gradient oracles, avoiding constraint‑specific projections. It uses fixed‑depth dual projected‑gradient descent on GPU‑friendly matrix operations to solve minimum‑displacement block problems, jointly learning a predictor and a positive‑definite mobility matrix to shape corrections. The method converges theoretically, achieves sub‑$10^{-3}$ feasibility on SOC‑MPC and power‑system relaxations, and outperforms state‑of‑the‑art constraint‑satisfaction techniques with up to 144× speedups and near‑optimal objective gaps.
By Haoyu Zhu, Xiaochen Zhang, Qingchun Hou