Singularity Degree of the Positive Semidefinite Matrix Completion Problem
نویسندگان
چکیده
منابع مشابه
Deterministic 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...
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We consider the decision problem asking whether a partial rational symmetric matrix with an all-ones diagonal can be completed to a full positive semidefinite matrix of rank at most k. We show that this problem is NP -hard for any fixed integer k ≥ 2. Equivalently, for k ≥ 2, it is NP -hard to test membership in the rank constrained elliptope Ek(G), i.e., the set of all partial matrices with of...
متن کاملFast 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 ...
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...
متن کاملAppendix: Active Positive Semidefinite Matrix Completion: Algorithms, Theory and Applications
We provide proofs that were skipped in the main paper. We also provide some additional experimental results and related work concerning multi-armed bandits that was skipped in the main paper.
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2017
ISSN: 1052-6234,1095-7189
DOI: 10.1137/16m1069262