The CP-matrix completion problem

2013/05/03 by Anwa Zhou, Zhou, Anwa, Jinyan Fan +1
Computer Science · Engineering · Mathematics · #15A48 #15A83 #90C22 #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Primary 15A23 #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1305.0632

openalex publication_date 2013/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A symmetric matrix C is completely positive (CP) if there exists an entrywise nonnegative matrix B such that C=BB^T. The CP-completion problem is to study whether we can assign values to the missing entries of a partial matrix (i.e., a matrix having unknown entries) such that the completed matrix is completely positive. We propose a semidefinite algorithm for solving general CP-completion problems, and study its properties. When all the diagonal entries are given, the algorithm can give a certificate if a partial matrix is not CP-completable, and it almost always gives a CP-completion if it is CP-completable. When diagonal entries are partially given, similar properties hold. Computational experiments are also presented to show how CP-completion problems can be solved.

Citations

• Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
• Matrix Completion With Noise

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