Solving large scale binary quadratic problems: Spectral methods vs. Semidefinite programming

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding


In this paper we introduce two new methods for solving binary quadratic problems. While spectral relaxation methods have been the workhorse subroutine for a wide variety of computer vision problems - segmentation, clustering, image restoration to name a few - it has recently been challenged by semidefinite programming (SDP) relaxations. In fact, it can be shown that SDP relaxations produce better lower bounds than spectral relaxations on binary problems with a quadratic objective junction. On the other hand, the computational complexity for SDP increases rapidly as the number of decision variables grows making them inapplicable to large scale problems. Our methods combine the merits of both spectral and SDP relaxations - better (lower) bounds than traditional spectral methods and considerably faster execution times than SDP The first method is based on spectral subgradients and can be applied to large scale SDPs with binary decision variables and the second one is based on the trust region problem. Both algorithms have been applied to several large scale vision problems with good performance.<sup>1</sup> © 2007 IEEE.


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics


  • Semidefinite programming, Quadratic objective junctions, Binary problems
Original languageEnglish
Title of host publicationProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
PublisherIEEE - Institute of Electrical and Electronics Engineers Inc.
Publication statusPublished - 2007
Publication categoryResearch
EventIEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2007 - Minneapolis, MN, United States
Duration: 2007 Jun 172007 Jun 22

Publication series

ISSN (Print)1063-6919


ConferenceIEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2007
Abbreviated titleCVPR'07
CountryUnited States
CityMinneapolis, MN