Preprint
Inexact Moreau Envelope Lagrangian Method for Non-Convex Constrained Optimization under Local Error Bound Conditions on Constraint Functions
ArXiV.org
Cornell University
02/27/2025
DOI: 10.48550/arxiv.2502.19764
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.
Details
- Title: Subtitle
- Inexact Moreau Envelope Lagrangian Method for Non-Convex Constrained Optimization under Local Error Bound Conditions on Constraint Functions
- Creators
- Yankun Huang - Arizona State UniversityQihang Lin - University of IowaYangyang Xu - Rensselaer Polytechnic Institute
- Resource Type
- Preprint
- Publication Details
- ArXiV.org
- DOI
- 10.48550/arxiv.2502.19764
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 02/27/2025
- Academic Unit
- Business Analytics
- Record Identifier
- 9984795375702771
Metrics
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