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Abstract: The purpose of this paper is to develop certain geometric results concerning the feasible regions of Semidefinite Programs, called here Spectrahedra. We first develop a characterization for the faces of spectrahedra. More specifically, given a point x in a spectrahedron, we derive an expression for the minimal face containing x. 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... (Update)
Context of citations to this paper: More
...be incomplete, X is not a singleton set. Next we study the facial structure of Omega Gamma (See also the theses [17, 18] and the papers [19, 16, 14] for characterizations for general sets) Definition 3.1 A matrix X 2 Omega is said to be an extreme point if X can not be...
.... proved independently by Barvinok [7] The faces of spectrahedra i.e. of feasible sets of SDP s were characterized by Ramana and Goldman [29]. Nondegeneracy and strict complementarity for SDP were introduced and studied by Shapiro and Fan [32] Alizadeh, Haeberly and Overton...
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BibTeX entry: (Update)
M.V. Ramana and A.J. Goldman, Some geometric results in semidefinite programming, Jnl. Glob. Opt., Vol. 7, pp. 33-50, 1995. http://citeseer.ist.psu.edu/ramana95some.html More
@article{ ramana95some,
author = "M. Ramana and A. J. Goldman",
title = "Some geometric results in semidefinite programming",
journal = "Journal of Global Optimization",
volume = "7",
number = "1",
pages = "33--50",
year = "1995",
url = "citeseer.ist.psu.edu/ramana95some.html" }
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230 Interior Point Methods in Semidefinite Programming with Appl.. - Alizadeh - 1995
60 Combinatorial Optimization with Interior Point Methods and S.. (context) - Alizadeh - 1991 ACM
49 Large-Scale Optimization of Eigenvalues - Overton - 1992 ACM
44 An algorithmic analysis of multiquadratic and semidefinite p.. (context) - Ramana - 1993
39 Optimality Conditions and Duality Theory for Minimizing Sums.. - Overton, Womersley - 1993 ACM
35 Some Applications of Optimization in Matrix Theory (context) - Wolkowicz - 1981
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30 Semi-Definite Matrix Constraints in Optimization (context) - Fletcher - 1985
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11 a Positive Semidefinite Relaxation of the Cut Polytope - Laurent, Poljak - 1993
9 Linear Algebra and its Applications (context) - Grone, Pierce et al. - 1990
9 the Facial Structure of Cone-LP's and Semidefinite Programs (context) - Pataki - 1994
8 Linear Algebra for Semidefinite Programming - Kojima, Kojima et al. - 1994
7 Duality and Asymptotic Solvability over Cones (context) - Ben-Israel, Charnes et al. - 1969
5 Simultaneous Diagonalization of Several Hermitian Matrices (context) - Binding - 1990
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2 Algorithms for Linear Programs over Cones and Semidefinite P.. (context) - Pataki - 1993
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1 Open Questions in Complexity Theory for Numerical Optimizati.. (context) - Pardalos, Vavasis - 1992 ACM
1 Cutting Plane Techniques for Multiquadratic Programming (context) - Ramana, Goldman
1 Quadratic Maps with Convex Images - Ramana, Goldman
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