Fast implementation for semidefinite programs with positive matrix completion
نویسندگان
چکیده
منابع مشابه
Fast implementation for semidefinite programs with positive matrix completion
Solving semidefinite programs (SDP) in a short time is the key to managing various mathematical optimization problems in practical time. The matrix-completion primal-dual interior-point method (MC-PDIPM) extracts a structural sparsity of input SDP by factorizing the variable matrices, and it shrinks the computation time. In this paper, we propose a new factorization based on the inverse of the ...
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Considering that preprocessing is an important phase in linear programming, it should be systematically more incorporated in semidefinite programming solvers. The conversion method proposed by the authors (SIAM Journal on Optimization, vol. 11, pp. 647–674, 2000, and Mathematical Programming, Series B, vol. 95, pp. 303–327, 2003) is a preprocessing of sparse semidefinite programs based on matri...
متن کاملDeterministic Symmetric Positive Semidefinite Matrix Completion
We consider the problem of recovering a symmetric, positive semidefinite (SPSD) matrix from a subset of its entries, possibly corrupted by noise. In contrast to previous matrix recovery work, we drop the assumption of a random sampling of entries in favor of a deterministic sampling of principal submatrices of the matrix. We develop a set of sufficient conditions for the recovery of a SPSD matr...
متن کاملA parallel primal-dual interior-point method for semidefinite programs using positive definite matrix completion
A parallel computational method SDPARA-C is presented for SDPs (semidefinite programs). It combines two methods SDPARA and SDPA-C proposed by the authors who developed a software package SDPA. SDPARA is a parallel implementation of SDPA and it features parallel computation of the elements of the Schur complement equation system and a parallel Cholesky factorization of its coefficient matrix. SD...
متن کاملAppendix for Deterministic Symmetric Positive Semidefinite Matrix Completion
First, note that by assumption rank{A} > 0. Let Ω1 = ρ1 × ρ1 and Ω2 = ρ2 × ρ2 be the two index sets in the theorem. By assumption we have ρ1 × ρ1 ∪ ρ2 × ρ2 = Ω and Ω 6= [n]× [n]. If A1 is not met, then ρ1 ∪ ρ2 6= [n], and from lemma 6 we can conclude recovery of A is impossible. If ρ1 ∪ ρ2 = [n], but A2 is not met then ι2 = |ρ1 ∩ ρ2| < r so it must be that rank{A(ι2, ι2)} < r. Further, by assum...
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ژورنال
عنوان ژورنال: Optimization Methods and Software
سال: 2015
ISSN: 1055-6788,1029-4937
DOI: 10.1080/10556788.2015.1014554