Title:
Accelerated algorithms for composite saddle-point problems and applications
Accelerated algorithms for composite saddle-point problems and applications
| dc.contributor.advisor | Park, Haesun | |
| dc.contributor.author | He, Yunlong | |
| dc.contributor.committeeMember | Monteiro, Renato D. C. | |
| dc.contributor.committeeMember | Zhou, Haomin | |
| dc.contributor.committeeMember | Kang, Sung Ha | |
| dc.contributor.committeeMember | Song, Le | |
| dc.contributor.department | Mathematics | |
| dc.date.accessioned | 2015-01-12T20:52:13Z | |
| dc.date.available | 2015-01-12T20:52:13Z | |
| dc.date.created | 2014-12 | |
| dc.date.issued | 2014-11-13 | |
| dc.date.submitted | December 2014 | |
| dc.date.updated | 2015-01-12T20:52:13Z | |
| dc.description.abstract | This dissertation considers the composite saddle-point (CSP) problem which is motivated by real-world applications in the areas of machine learning and image processing. Two new accelerated algorithms for solving composite saddle-point problems are introduced. Due to the two-block structure of the CSP problem, it can be solved by any algorithm belonging to the block-decomposition hybrid proximal extragradient (BD-HPE) framework. The framework consists of a family of inexact proximal point methods for solving a general two-block structured monotone inclusion problem which, at every iteration, solves two prox sub-inclusions according to a certain relative error criterion. By exploiting the fact that the two prox sub-inclusions in the context of the CSP problem are equivalent to two composite convex programs, the first part of this dissertation proposes a new instance of the BD-HPE framework that approximately solves them using an accelerated gradient method. It is shown that this new instance has better iteration-complexity than the previous ones. The second part of this dissertation introduces a new algorithm for solving a special class of CSP problems. The new algorithm is a special instance of the hybrid proximal extragradient (HPE) framework in which a Nesterov's accelerated variant is used to approximately solve the prox subproblems. One of the advantages of the this method is that it works for any constant choice of proximal stepsize. Moreover, a suitable choice of the latter stepsize yields a method with the best known (accelerated inner) iteration complexity for the aforementioned class of saddle-point problems. Experiment results on both synthetic CSP problems and real-world problems show that the two method significantly outperform several state-of-the-art algorithms. | |
| dc.description.degree | Ph.D. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/1853/53069 | |
| dc.language.iso | en_US | |
| dc.publisher | Georgia Institute of Technology | |
| dc.subject | Saddle-point problem | |
| dc.subject | Composite optimization | |
| dc.subject | Accelerated algorithm | |
| dc.subject | Machine learning | |
| dc.subject | Image processing | |
| dc.title | Accelerated algorithms for composite saddle-point problems and applications | |
| dc.type | Text | |
| dc.type.genre | Dissertation | |
| dspace.entity.type | Publication | |
| local.contributor.advisor | Park, Haesun | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Mathematics | |
| relation.isAdvisorOfPublication | 92013a6f-96b2-4ca8-9ef7-08f408ec8485 | |
| relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
| relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 | |
| thesis.degree.level | Doctoral |