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Nonconvex Quadratic Programming, Semidefinite Relaxations and Randomization Algorithms in Information and Decision Systems

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System Theory

Part of the book series: The Springer International Series in Engineering and Computer Science ((SECS,volume 518))

Abstract

Nonconvex quadratic optimization problems and the methods for their analysis have been on the center stage of information and decision systems for the past 50 years. Although most of these problems are very complex in general, all of them may be relaxed to semidefinite programs. In many cases, this relaxation is tight or it may be bounded. The solution to those programs facilitates the solution to the original nonconvex problem, notably via efficient randomization techniques. Engineering applications of nonconvex quadratic programming and related solution techniques are virtually infinite. Examples extracted from the current literature on information and decision systems are provided. These examples include network optimization problems, linear and nonlinear control problems and important linear algebra problems.

Research funded by NASA (NCC2-1044), ONR (N00014-99-1-0668) and Draper Laboratory (DL-H-505334).

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Authors and Affiliations

  1. Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Eric Feron

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  1. Eric Feron
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Editor information

Editors and Affiliations

  1. University of Massachusetts Amherst, USA

    Theodore E. Djaferis

  2. GTE Internetworking, USA

    Irvin C. Schick

  3. Harvard University, USA

    Irvin C. Schick

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Feron, E. (2000). Nonconvex Quadratic Programming, Semidefinite Relaxations and Randomization Algorithms in Information and Decision Systems. In: Djaferis, T.E., Schick, I.C. (eds) System Theory. The Springer International Series in Engineering and Computer Science, vol 518. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5223-9_19

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  • DOI: https://doi.org/10.1007/978-1-4615-5223-9_19

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7380-3

  • Online ISBN: 978-1-4615-5223-9

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