Farid Alizadeh Jean-Pierre A. Haeberly Michael L. Overton March 1995...  Home/Search
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Abstract: Primal and dual nondegeneracy conditions are defined for semidefinite programming. Given the existence of primal and dual solutions, it is shown that primal nondegeneracy implies a unique dual solution and that dual nondegeneracy implies a unique primal solution. The converses hold if strict complementarity is assumed. Primal and dual nondegeneracy assumptions do not imply strict complementarity, as they do in LP. The primal and dual nondegeneracy assumptions imply a range of possible ranks for ... (Update)
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...side of (2.10) under nondegeneracy assumptions. To do this, we use the notions of nondegeneracy that were introduced by the authors in [3]. DEFINITION 1. Let (X,y,Z) solve (1.2) 1.3) with an orthogonal matrix Q satisfying (1.9) LetX have rank r, with positive eigenvalues #...
...(X # , y # , Z # ) of the primal and dual SDP. If (X # , Z # ) satisfies the strict complementarity condition defined in [1] (that is, rank(X # ) rank(Z # ) n) then as (X, Z) approaches this optimal solution (i.e. when is su#ciently small) the eigenvalues of W will...
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BibTeX entry: (Update)
W. F. Alizadeh, J. -P. A. Haeberly and M. L. Overton, , "Complementarity and Nondegeneracy in Semidefinite Programming," Working Paper, 1995. http://citeseer.ist.psu.edu/article/alizadeh95complementarity.html More
@techreport{ alizadeh95complementarity,
author = "F. Alizadeh and J.--P. A. Haeberly and M. L. Overton",
title = "Complementarity and nondegeneracy in semidefinite programming",
address = "New Brunswick, NJ~08903, USA",
year = "1995",
url = "citeseer.ist.psu.edu/article/alizadeh95complementarity.html" }
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