The CP-matrix Approximation Problem

2014/11/04 by Jinyan Fan, Fan, Jinyan, Anwa Zhou +1
Computer Science · Engineering · Mathematics · #90C20 #90C22 #90C26 #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1411.0795

openalex publication_date 2014/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A symmetric matrix A is completely positive (CP) if there exists an entrywise nonnegative matrix V such that A = V V ^T. In this paper, we study the CP-matrix approximation problem of projecting a matrix onto the intersection of a set of linear constraints and the cone of CP matrices. We formulate the problem as the linear optimization with the norm cone and the cone of moments. A semidefinite algorithm is presented for the problem. A CP-decomposition of the projection matrix can also be obtained if the problem is feasible.

Related

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• Interiors of completely positive cones
• Inner approximating the completely positive cone via the cone of scaled diagonally dominant matrices
• Optimization over Structured Subsets of Positive Semidefinite Matrices via Column Generation
• On generators of k-PSD closures of the positive semidefinite cone