arXiv AI
Operational Regimes in Non-Convex Optimization: A Multiplier-Based Taxonomy
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arXiv Machine Learning
Jul 13
Nonconvex Composite Functional Constraints via First-Order Augmented Lagrangian Methods under Local Regularity
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 Machine Learning
Sep 15
Equilibrium bias and convergence in augmented primal--dual dynamics with sampled constraints
arXiv:2609.13925v1 Announce Type: cross Abstract: This work studies the stability and convergence of augmented primal-dual dynamics when constraint values are estimated from samples. Unbiased constra...
arXiv Machine Learning
Jul 13
Accelerated Fully First-Order Methods for Bilevel and Minimax Optimization
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 Machine Learning
Jul 8
Stability Annealing Selects the Implicit Bias of Smoothed Sign Descent: A Rate-Indexed Barrier Path on Separable Data
arXiv:2607. 06013v1 Announce Type: new Abstract: Adaptive gradient methods can favor max-margin separators that differ from gradient descent, yet a fixed positive numerical stability constant eventually changes the update geometry again.
arXiv Machine Learning
Jun 29
Second-Order KKT Guarantees for Bregman ADMM in Nonconvex and Non-Lipschitz Optimization
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 Machine Learning
Jul 9
Geometric--Nongeometric Optimizer Calculus: A Modular Language for Reachable Gradient Methods
arXiv:2607. 07206v1 Announce Type: new Abstract: Adaptive optimizers mix several mechanisms: a metric or preconditioner maps gradients to descent directions, while estimation, memory, step-size control, constraints, stochasticity, target modification, and discretization determine which directions are available and how they are used.