Proximal point algorithm with Schur decomposition on the cone of symmetric semidefinite positive matrices
نویسندگان
چکیده
منابع مشابه
Proximal Point Algorithm with Schur Decomposition on the Cone of Symmetric Semidefinite Positive Matrices∗
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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Suppose that A ∈ RN×N is symmetric positive semidefinite with rank K ≤ N . Our goal is to decompose A into K rank-one matrices ∑K k=1 gkg T k where the modes {gk} K k=1 are required to be as sparse as possible. In contrast to eigen decomposition, these sparse modes are not required to be orthogonal. Such a problem arises in random field parametrization where A is the covariance function and is ...
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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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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2009
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2009.02.006