Journal of Global Optimization

, Volume 7, Issue 1, pp 33–50

Some geometric results in semidefinite programming

  • Motakuri Ramana
  • A. J. Goldman

DOI: 10.1007/BF01100204

Cite this article as:
Ramana, M. & Goldman, A.J. J Glob Optim (1995) 7: 33. doi:10.1007/BF01100204


The purpose of this paper is to develop certain geometric results concerning the feasible regions of Semidefinite Programs, called hereSpectrahedra.

We first develop a characterization for the faces of spectrahedra. More specifically, given a pointx in a spectrahedron, we derive an expression for the minimal face containingx. Among other things, this is shown to yield characterizations for extreme points and extreme rays of spectrahedra. We then introduce the notion of an algebraic polar of a spectrahedron, and present its relation to the usual geometric polar.

Key words

Semidefinite programming convex geometry 

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Motakuri Ramana
    • 1
  • A. J. Goldman
    • 2
  1. 1.Center for Operations Research (RUTCOR)Rutgers UniversityNew BrunswickUSA
  2. 2.Mathematical Sciences DepartmentThe Johns Hopkins UniversityBaltimoreUSA

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