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.
arXiv:2609.00471v1 Announce Type: cross Abstract: This paper introduces a structural taxonomy for constrained non-convex optimization based on the signature of Lagrange multipliers at KKT stationary...
arXiv:2605. 08488v2 Announce Type: replace-cross Abstract: We develop a unified Lyapunov-integral quadratic constraint (IQC) framework for establishing uniform stability of first-order accelerated optimization algorithms in the $\beta$-smooth and $\gamma$-strongly convex regime.
arXiv:2606. 07088v1 Announce Type: new Abstract: Stochastic constrained decision-making requires optimizing performance objectives while enforcing statistical requirements such as safety or fairness.
arXiv:2606. 28307v1 Announce Type: cross Abstract: We analyze Bregman ADMM for nonconvex linearly constrained problems under two-sided relative smoothness, a condition that replaces the standard Lipschitz gradient assumption with a Hessian comparison relative to a Bregman kernel.
arXiv:2606. 31182v1 Announce Type: new Abstract: Recent work shows that LLM agents can improve sharp-constant inequalities by searching for extremal constructions, which yield upper bounds.
arXiv:2509.02894v2 Announce Type: replace-cross Abstract: We propose an inexact proximal augmented Lagrangian method (P-ALM) for nonconvex structured optimization problems. The proposed method featur...
arXiv:2606. 25012v1 Announce Type: new Abstract: Many reinforcement learning (RL) problems in the infinite-horizon average-reward setting require optimizing multiple conflicting objectives while satisfying multiple safety constraints.
arXiv:2608. 05502v1 Announce Type: cross Abstract: In this paper, we consider a class of multiblock nonconvex nonsmooth optimization problems, which covers many applications such as the analysis of pre-earthquake anomalies and machine learning.
arXiv:2609.36310v1 Announce Type: new Abstract: Everywhere learning provides a principled framework for training AI models under constraints that must hold throughout the data distribution. In the du...
arXiv:2406. 13041v3 Announce Type: replace Abstract: Lower-bound analyses for nonconvex strongly-concave minimax optimization problems have shown that stochastic first-order algorithms require at least $\mathcal{O}(\varepsilon^{-4})$ sample complexity to find an $\varepsilon$-stationary point.
arXiv:2608. 12665v1 Announce Type: cross Abstract: For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.