arXiv Machine Learning
Accelerated Frank-Wolfe Algorithms: Complementarity Conditions and Sparsity
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arXiv Machine Learning
Oct 9
Composite Online-to-Nonconvex Conversion with Optimal Oracle Complexity
arXiv:2610. 12328v1 Announce Type: new Abstract: We consider stochastic nonsmooth nonconvex composite optimization, which includes several important problems such as constrained optimization and the regularized training of neural networks.
arXiv Machine Learning
Oct 19
Guarded Block Transfers for Polytope Distance: Linear Convergence with Explicit Constants and Gap-Certified Screening for SVM Training
arXiv:2610.15829v2 Announce Type: replace Abstract: Hard-margin SVM training is the distance problem between two convex hulls, which the Triangle Algorithm (TA) solves with a certified duality gap. W...
arXiv Machine Learning
Aug 4
The Condition-Number Barrier in Sparse Least Squares
arXiv:2608. 02588v1 Announce Type: cross Abstract: In [AS21], Axiotis and Sviridenko conjectured that the linear dependence on the restricted condition number in sparse convex optimization cannot be improved by a polynomial-time algorithm.
arXiv Machine Learning
Jul 21
Exploiting Low-Rank Objective Structure in Discrete Quadratic Optimization
arXiv:2602. 20376v3 Announce Type: replace-cross Abstract: We study the problem of maximizing a complex-valued quadratic form over the $K^{\text{th}}$ roots of unity.
arXiv Machine Learning
Sep 22
Complexities of Weak Proximal Oracle Methods for Composite Convex Optimization
arXiv:2609.24423v1 Announce Type: cross Abstract: We consider a standard convex composite optimization problem with either smooth or nonsmooth objective function, and under quadratic growth. In recen...
arXiv AI
2d ago
Convex-SKM-Net: Low-Latency Block Halfspace Corrections for Neural Convex Constraint Satisfaction
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.