Generalized S-Lemma and strong duality in nonconvex quadratic programming

Tuy, H; Tuan, HD

Generalized S-Lemma and strong duality in nonconvex quadratic programming

Tuy, H Tuan, HD

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Publication Type:: Journal Article
Citation:: Journal of Global Optimization, 2013, 56 (3), pp. 1045 - 1072
Issue Date:: 2013-07-01

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Field	Value	Language
dc.contributor.author	Tuy, H	en_US
dc.contributor.author	Tuan, HD https://orcid.org/0000-0003-0292-6061	en_US
dc.date.issued	2013-07-01	en_US
dc.identifier.citation	Journal of Global Optimization, 2013, 56 (3), pp. 1045 - 1072	en_US
dc.identifier.issn	0925-5001	en_US
dc.identifier.uri	http://hdl.handle.net/10453/26582
dc.description.abstract	On the basis of a new topological minimax theorem, a simple and unified approach is developed to Lagrange duality in nonconvex quadratic programming. Diverse generalizations as well as equivalent forms of the S-Lemma, providing a thorough study of duality for single constrained quadratic optimization, are derived along with new strong duality conditions for multiple constrained quadratic optimization. The results allow many quadratic programs to be solved by solving one or just a few SDP's (semidefinite programs) of about the same size, rather than solving a sequence, often infinite, of SDP's or linear programs of a very large size as in most existing methods. © 2012 Springer Science+Business Media, LLC.	en_US
dc.relation.ispartof	Journal of Global Optimization	en_US
dc.relation.isbasedon	10.1007/s10898-012-9917-0	en_US
dc.subject.classification	Operations Research	en_US
dc.title	Generalized S-Lemma and strong duality in nonconvex quadratic programming	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	56	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0103 Numerical and Computational Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
utslib.copyright.status	closed_access
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	56	en_US

Abstract:

On the basis of a new topological minimax theorem, a simple and unified approach is developed to Lagrange duality in nonconvex quadratic programming. Diverse generalizations as well as equivalent forms of the S-Lemma, providing a thorough study of duality for single constrained quadratic optimization, are derived along with new strong duality conditions for multiple constrained quadratic optimization. The results allow many quadratic programs to be solved by solving one or just a few SDP's (semidefinite programs) of about the same size, rather than solving a sequence, often infinite, of SDP's or linear programs of a very large size as in most existing methods. © 2012 Springer Science+Business Media, LLC.

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http://hdl.handle.net/10453/26582