FOUNDATIONS OF GAUGE AND PERSPECTIVE DUALITY.
Saved in:
| Title: | FOUNDATIONS OF GAUGE AND PERSPECTIVE DUALITY. |
|---|---|
| Authors: | ARAVKIN, A. Y.1 sasha.aravkin@gmail.com, BURKE, J. V.2 jvburke01@gmail.com, DRUSVYATSKIY, D.2 ddrusv@uw.edu, FRIEDLANDER, M. P.3 mpf@cs.ubc.ca, MACPHEE, K. J.3 kmacphee@uw.edu |
| Source: | SIAM Journal on Optimization. 2018, Vol. 28 Issue 3, p2406-2434. 29p. |
| Subjects: | Gauge field theory, Duality theory (Mathematics), Perturbation theory, Convex functions, Quadratic programming, Regression analysis |
| Abstract: | We revisit the foundations of gauge duality and demonstrate that it can be explained using a modern approach to duality based on a perturbation framework. We therefore put gauge duality and Fenchel--Rockafellar duality on equal footing, including explaining gauge dual variables as sensitivity measures, and show how to recover primal solutions from those of the gauge dual. This vantage point allows a direct proof that optimal solutions of the Fenchel--Rockafellar dual of the gauge dual are precisely the primal solutions rescaled by the optimal value. We extend the gauge duality framework to the setting in which the functional components are general nonnegative convex functions, including problems with piecewise linear quadratic functions and constraints that arise from generalized linear models used in regression. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 132350820 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: FOUNDATIONS OF GAUGE AND PERSPECTIVE DUALITY. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22ARAVKIN%2C+A%2E+Y%2E%22">ARAVKIN, A. Y.</searchLink><relatesTo>1</relatesTo><i> sasha.aravkin@gmail.com</i><br /><searchLink fieldCode="AR" term="%22BURKE%2C+J%2E+V%2E%22">BURKE, J. V.</searchLink><relatesTo>2</relatesTo><i> jvburke01@gmail.com</i><br /><searchLink fieldCode="AR" term="%22DRUSVYATSKIY%2C+D%2E%22">DRUSVYATSKIY, D.</searchLink><relatesTo>2</relatesTo><i> ddrusv@uw.edu</i><br /><searchLink fieldCode="AR" term="%22FRIEDLANDER%2C+M%2E+P%2E%22">FRIEDLANDER, M. P.</searchLink><relatesTo>3</relatesTo><i> mpf@cs.ubc.ca</i><br /><searchLink fieldCode="AR" term="%22MACPHEE%2C+K%2E+J%2E%22">MACPHEE, K. J.</searchLink><relatesTo>3</relatesTo><i> kmacphee@uw.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Optimization%22">SIAM Journal on Optimization</searchLink>. 2018, Vol. 28 Issue 3, p2406-2434. 29p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Gauge+field+theory%22">Gauge field theory</searchLink><br /><searchLink fieldCode="DE" term="%22Duality+theory+%28Mathematics%29%22">Duality theory (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Perturbation+theory%22">Perturbation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+functions%22">Convex functions</searchLink><br /><searchLink fieldCode="DE" term="%22Quadratic+programming%22">Quadratic programming</searchLink><br /><searchLink fieldCode="DE" term="%22Regression+analysis%22">Regression analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We revisit the foundations of gauge duality and demonstrate that it can be explained using a modern approach to duality based on a perturbation framework. We therefore put gauge duality and Fenchel--Rockafellar duality on equal footing, including explaining gauge dual variables as sensitivity measures, and show how to recover primal solutions from those of the gauge dual. This vantage point allows a direct proof that optimal solutions of the Fenchel--Rockafellar dual of the gauge dual are precisely the primal solutions rescaled by the optimal value. We extend the gauge duality framework to the setting in which the functional components are general nonnegative convex functions, including problems with piecewise linear quadratic functions and constraints that arise from generalized linear models used in regression. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Optimization is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=132350820 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/17M1119020 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 29 StartPage: 2406 Subjects: – SubjectFull: Gauge field theory Type: general – SubjectFull: Duality theory (Mathematics) Type: general – SubjectFull: Perturbation theory Type: general – SubjectFull: Convex functions Type: general – SubjectFull: Quadratic programming Type: general – SubjectFull: Regression analysis Type: general Titles: – TitleFull: FOUNDATIONS OF GAUGE AND PERSPECTIVE DUALITY. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: ARAVKIN, A. Y. – PersonEntity: Name: NameFull: BURKE, J. V. – PersonEntity: Name: NameFull: DRUSVYATSKIY, D. – PersonEntity: Name: NameFull: FRIEDLANDER, M. P. – PersonEntity: Name: NameFull: MACPHEE, K. J. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: 2018 Type: published Y: 2018 Identifiers: – Type: issn-print Value: 10526234 Numbering: – Type: volume Value: 28 – Type: issue Value: 3 Titles: – TitleFull: SIAM Journal on Optimization Type: main |
| ResultId | 1 |
