Journal article
An Inexact Primal-Dual Smoothing Framework for Large-Scale Non-Bilinear Saddle Point Problems
Journal of optimization theory and applications, Vol.200(1), pp.34-67
01/2024
DOI: 10.1007/s10957-023-02351-9
Abstract
We develop an inexact primal-dual first-order smoothing framework to solve a class of non-bilinear saddle point problems with primal strong convexity. Compared with existing methods, our framework yields a significant improvement over the primal oracle complexity, while it has competitive dual oracle complexity. In addition, we consider the situation where the primal-dual coupling term has a large number of component functions. To efficiently handle this situation, we develop a randomized version of our smoothing framework, which allows the primal and dual sub-problems in each iteration to be inexactly solved by randomized algorithms in expectation. The convergence of this framework is analyzed both in expectation and with high probability. In terms of the primal and dual oracle complexities, this framework significantly improves over its deterministic counterpart. As an important application, we adapt both frameworks for solving convex optimization problems with many functional constraints. To obtain an -optimal and -feasible solution, both frameworks achieve the best-known oracle complexities.
Details
- Title: Subtitle
- An Inexact Primal-Dual Smoothing Framework for Large-Scale Non-Bilinear Saddle Point Problems
- Creators
- Le Thi Khanh Hien - University of MonsRenbo Zhao - University of IowaWilliam B. Haskell - Purdue University West Lafayette
- Resource Type
- Journal article
- Publication Details
- Journal of optimization theory and applications, Vol.200(1), pp.34-67
- DOI
- 10.1007/s10957-023-02351-9
- ISSN
- 0022-3239
- eISSN
- 1573-2878
- Language
- English
- Electronic publication date
- 12/22/2023
- Date published
- 01/2024
- Academic Unit
- Business Analytics
- Record Identifier
- 9984539526202771
Metrics
2 Record Views