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: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: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: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: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...
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.
arXiv:2405. 00914v4 Announce Type: replace-cross Abstract: We present in this paper novel accelerated fully first-order methods in \emph{Bilevel Optimization} (BLO).
arXiv:2608. 08463v1 Announce Type: cross Abstract: We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI).
arXiv:2610. 03222v1 Announce Type: cross Abstract: This paper studies the complexity of convex optimization using lazy second-order oracles (Doikov, Chayti, and Jaggi, ICML 2023), where an algorithm queries gradients every iteration and Hessians once per $m$ iterations.
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. We establish their conjectured lower bound for least-squares objectives, conditional on the randomized exact-volume Small-Set Expansion Hypothesis in the weighted regular-graph formulation of Raghavendra, Steurer, and Tulsiani [RST12].
arXiv:2607. 08954v1 Announce Type: cross Abstract: We study nonasymptotic convergence of primal-dual methods for a class of nonconvex constrained optimization problems with a convex-composite structure.
In this work, we study the oracle complexity of finding an $ε$-stationary point for nonconvex-strongly-convex (NC-SC) bilevel optimization using only first-order oracles. Existing methods achieving th...