Nonconvex Composite Functional Constraints via First-Order Augmented Lagrangian Methods under Local Regularity

arXiv:2607.08954 · math.OC, cs.LG, stat.ML · Submitted 2026-07-09 · Read on arXiv

math.OC, cs.LG, stat.ML

Submitted: 2026-07-09

Updated: 2026-10-14

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Regularization — 10× in this paper · explained in 3 episodes
• Absorb — 3× in this paper · explained in 1 episode
• Composition — 2× in this paper · explained in 2 episodes
• Clarity — 1× in this paper · explained in 3 episodes
• KKT conditions — 1× in this paper · explained in 2 episodes
• Localization — 1× in this paper · explained in 2 episodes
• Lyapunov function — 1× in this paper · explained in 2 episodes

Sources

• Inexact Moreau Envelope Lagrangian Method for Non-Convex Constrained Optimization under Local Error Bound Conditions on Constraint Functions
• Smoothing Meets Perturbation: Unified and Tight Analysis for Nonconvex-Concave Minimax Optimization
• Smoothed Proximal Lagrangian Method for Nonlinear Constrained Programs
• Primal-Dual Methods for Nonsmooth Nonconvex Optimization with Orthogonality Constraints

Related papers

• Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise
• Adam-HNAG: A Convergent Reformulation of Adam with Accelerated Rate
• Incremental Learning in Mirror Flows
• Beyond Aggregate Drift: Optimal Client-Specific Windows in Federated Learning
• Lower Bounds for Randomized Linear-Oracle Optimization over Strongly Convex Sets
• Second-Order Optimization with Asynchronous Curvature