Rank Restricted Semidefinite Matrices and Image Closedness

2016/10/31 by Ian Davidson, Davidson, Ian, Henry Wolkowicz +1
Computer Science · Engineering · #52A99 #90C22 #90C46 #FOS: Mathematics #Face and Expression Recognition #Medical Image Segmentation Techniques #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1610.09993

openalex publication_date 2016/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the closure of the projection of the (nonconvex) cone of rank restricted positive semidefinite matrices onto subsets of the matrix entries. This defines the feasible sets for semidefinite completion problems with restrictions on the ranks. Applications include conditions for low-rank completions using the nuclear norm heuristic.

Citations

• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization

Related

• Complexity of the positive semidefinite matrix completion problem with a\n rank constraint
• Rational and real positive semidefinite rank can be different
• Necessary and sufficient conditions for rank-one generated cones
• Low-Rank Matrix Completion using Nuclear Norm with Facial Reduction
• A Class of Semidefinite Programs with rank-one solutions