Papers › First-Order Methods for Nonsmooth Nonconvex Functional Constrained Optimization with...
First-Order Methods for Nonsmooth Nonconvex Functional Constrained Optimization with or without Slater Points
Zhichao Jia, Benjamin Grimmer
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Constrained optimization problems where both the objective and constraints may be nonsmooth and nonconvex arise across many learning and data science settings. In this paper, we show for any Lipschitz, weakly convex objectives and constraints, a simple first-order method finds a feasible, ϵ-stationary point at a convergence rate of O(ϵ⁻⁴) without relying on compactness or Constraint Qualification (CQ). When CQ holds, this convergence is measured by approximately satisfying the Karush-Kuhn-Tucker conditions. When CQ fails, we guarantee the attainment of weaker Fritz-John conditions. As an illustrative example, our method stably converges on piecewise quadratic SCAD regularized problems despite frequent violations of constraint qualification. The considered algorithm is similar to those of "Quadratically regularized subgradient methods for weakly convex optimization with weakly convex constraints" by Ma et al. and "Stochastic first-order methods for convex and nonconvex functional constrained optimization" by Boob et al. (whose guarantees further assume compactness and CQ), iteratively taking inexact proximal steps, computed via an inner loop applying a switching subgradient method to a strongly convex constrained subproblem. Our non-Lipschitz analysis of the switching subgradient method appears to be new and may be of independent interest.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections