Efficient projected gradient methods for cardinality constrained optimization

2018 ◽  
Vol 62 (2) ◽  
pp. 245-268
Author(s):  
Fengmin Xu ◽  
Yuhong Dai ◽  
Zhihu Zhao ◽  
Zongben Xu
2000 ◽  
Vol 10 (4) ◽  
pp. 1196-1211 ◽  
Author(s):  
Ernesto G. Birgin ◽  
José Mario Martínez ◽  
Marcos Raydan

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

2007 ◽  
Vol 19 (10) ◽  
pp. 2756-2779 ◽  
Author(s):  
Chih-Jen Lin

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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