Low-Rank Optimization on the Cone of Positive Semidefinite Matrices
نویسندگان
چکیده
منابع مشابه
Low-Rank Optimization on the Cone of Positive Semidefinite Matrices
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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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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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2010
ISSN: 1052-6234,1095-7189
DOI: 10.1137/080731359