A penalty method for rank minimization problems in symmetric matrices

• Published in: Computational optimization and applications Vol. 71; no. 2; pp. 353 - 380
• Main Authors: Shen, Xin, Mitchell, John E.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2018; Springer Nature B.V
• Subjects: Convex and Discrete Geometry; Management Science; Mathematics; Mathematics and Statistics; Matrix methods; Operations Research; Operations Research/Decision Theory; Optimization; Statistics; 90C53; Penalty methods; Alternating minimization; 90C33; Rank minimization

The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive semidefinite matrices to be complementary. This is a continuous a...