A new approximation of the matrix rank function and its application to matrix rank minimization

DOI10.1007/s10957-013-0477-3zbMath1317.90280OpenAlexW2012688283MaRDI QIDQ481777

Chengjin Li

Publication date: 15 December 2014

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-013-0477-3

zbMATH Keywords

projected gradient methodapproximation functionmatrix rank minimizationsuccessive projected gradient method

Mathematics Subject Classification ID

Nonlinear programming (90C30) Determinants, permanents, traces, other special matrix functions (15A15) Methods of reduced gradient type (90C52)

Cites Work

• Unnamed Item
• Approximation of rank function and its application to the nearest low-rank correlation matrix
• An approximation theory of matrix rank minimization and its application to quadratic equations
• An implementable proximal point algorithmic framework for nuclear norm minimization
• Fixed point and Bregman iterative methods for matrix rank minimization
• Convex optimization methods for dimension reduction and coefficient estimation in multivariate linear regression
• Nuclear norm minimization for the planted clique and biclique problems
• Merit functions for semi-definite complementarity problems
• Distance matrix completion by numerical optimization
• The geometry of graphs and some of its algorithmic applications
• Rank-one solutions for homogeneous linear matrix equations over the positive semidefinite cone
• Optimization theory and methods. Nonlinear programming
• Exact matrix completion via convex optimization
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• Smoothing Projected Gradient Method and Its Application to Stochastic Linear Complementarity Problems
• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• Projected gradient methods for linearly constrained problems
• Global and Asymptotic Convergence Rate Estimates for a Class of Projected Gradient Processes
• On the rank minimization problem over a positive semidefinite linear matrix inequality
• A Spectral Bundle Method for Semidefinite Programming
• The Power of Convex Relaxation: Near-Optimal Matrix Completion
• The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications
• Convex programming in Hilbert space
• Semismooth Matrix-Valued Functions

This page was built for publication: A new approximation of the matrix rank function and its application to matrix rank minimization