منابع مشابه
Positive Semidefinite Germs on the Cone
The problem of representing a positive semidefinite function (=psd) as a sum of squares (=sos) is a very old matter in real algebra and real geometry. Still, it is a difficult question always appealing the specialists. Concerning real analytic germs we can summarize what is known in a few statements. Let X be a irreducible real analytic set germ of dimension d. Any psd f of X is an sos of merom...
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We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = Y ...
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The positive semideenite constraint for the variable matrix in semideenite programming (SDP) relaxation is further relaxed by a nite number of second order cone constraints in second order cone programming (SOCP) relaxations. A few types of SOCP relaxations are obtained from diierent ways of expressing the positive semideenite constraint of the SDP relaxation. We present how such SOCP relaxatio...
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The structural properties of the completely positive semidefinite cone CS+, consisting of all the n×n symmetric matrices that admit a Gram representation by positive semidefinite matrices of any size, are investigated. This cone has been introduced to model quantum graph parameters as conic optimization problems. Recently it has also been used to characterize the set Q of bipartite quantum corr...
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In this work, we propose a proximal algorithm for unconstrained optimization on the cone of symmetric semidefinite positive matrices. It appears to be the first in the proximal class on the set of methods that convert a Symmetric Definite Positive Optimization in Nonlinear Optimization. It replaces the main iteration of the conceptual proximal point algorithm by a sequence of nonlinear programm...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2002
ISSN: 0030-8730
DOI: 10.2140/pjm.2002.205.109