Journal article
A Primal-Dual Smoothing Framework for Max-Structured Non-Convex Optimization
Mathematics of operations research, Vol.49(3), pp.1535-1565
09/08/2023
DOI: 10.1287/moor.2023.1387
Abstract
We propose a primal-dual smoothing framework for finding a near-stationary point of a class of nonsmooth nonconvex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two approaches, that is, the dual-then-primal and primal-the-dual smoothing approaches. Our framework improves the best-known oracle complexities of the existing method, even in the restricted problem setting. As an important part of our framework, we propose a first-order method for solving a class of (strongly) convex-concave saddle-point problems, which is based on a newly developed non-Hilbertian inexact accelerated proximal gradient algorithm for strongly convex composite minimization that enjoys duality-gap convergence guarantees. Some variants and extensions of our framework are also discussed. Funding: R. Zhao’s research is partially supported by AFOSR [Grant FA9550-22-1-0356].
Details
- Title: Subtitle
- A Primal-Dual Smoothing Framework for Max-Structured Non-Convex Optimization
- Creators
- Renbo Zhao - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Mathematics of operations research, Vol.49(3), pp.1535-1565
- DOI
- 10.1287/moor.2023.1387
- ISSN
- 0364-765X
- eISSN
- 1526-5471
- Publisher
- Informs
- Language
- English
- Electronic publication date
- 09/08/2023
- Academic Unit
- Business Analytics
- Record Identifier
- 9984466659502771
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