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Inexact Moreau Envelope Lagrangian Method for Non-Convex Constrained Optimization under Local Error Bound Conditions on Constraint Functions
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Inexact Moreau Envelope Lagrangian Method for Non-Convex Constrained Optimization under Local Error Bound Conditions on Constraint Functions

Yankun Huang, Qihang Lin and Yangyang Xu
ArXiV.org
Cornell University
02/27/2025
DOI: 10.48550/arxiv.2502.19764
url
https://doi.org/10.48550/arxiv.2502.19764View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In this paper, we study the inexact Moreau envelope Lagrangian (iMELa) method for solving smooth non-convex optimization problems over a simple polytope with additional convex inequality constraints. By incorporating a proximal term into the traditional Lagrangian function, the iMELa method approximately solves a convex optimization subproblem over the polyhedral set at each main iteration. Under the assumption of a local error bound condition for subsets of the feasible set defined by subsets of the constraints, we establish that the iMELa method can find an ϵ-Karush-Kuhn-Tucker point with O~(ϵ−2) gradient oracle complexity.
Computer Science - Learning Mathematics - Optimization and Control

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