scholarly journals On the Convergence of Projected-Gradient Methods with Low-Rank Projections for Smooth Convex Minimization over Trace-Norm Balls and Related Problems

2021 ◽  
Vol 31 (1) ◽  
pp. 727-753
Author(s):  
Dan Garber
Keyword(s):  
Gradient Methods ◽  
Convex Minimization ◽  
Low Rank ◽  
Trace Norm ◽  
Smooth Convex ◽  
Projected Gradient ◽  
Projected Gradient Methods ◽  
Smooth Convex Minimization

scholarly journals Nonmonotone Spectral Projected Gradient Methods on Convex Sets

2000 ◽  
Vol 10 (4) ◽  
pp. 1196-1211 ◽  
Author(s):  
Ernesto G. Birgin ◽  
José Mario Martínez ◽  
Marcos Raydan
Keyword(s):  
Convex Sets ◽  
Gradient Methods ◽  
Projected Gradient ◽  
Spectral Projected Gradient ◽  
Projected Gradient Methods

scholarly journals Spectral Projected Gradient Methods

2008 ◽  
pp. 3652-3659 ◽  
Author(s):  
Ernesto G. Birgin ◽  
J. M. Martínez ◽  
Marcos Raydan
Keyword(s):  
Gradient Methods ◽  
Projected Gradient ◽  
Spectral Projected Gradient ◽  
Projected Gradient Methods

scholarly journals Projected Gradient Methods for Nonnegative Matrix Factorization

2007 ◽  
Vol 19 (10) ◽  
pp. 2756-2779 ◽  
Author(s):  
Chih-Jen Lin
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Gradient Methods ◽  
Nonnegative Matrix ◽  
Theory And Practice ◽  
Bound Constraints ◽  
Projected Gradient ◽  
Matlab Code ◽  
Projected Gradient Methods ◽  
Multiplicative Update

Nonnegative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this letter, we propose two projected gradient methods for NMF, both of which exhibit strong optimization properties. We discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach. A simple Matlab code is also provided.

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