A Symmetric Rank-One Quasi-Newton Method for Nonnegative Matrix Factorization

Algorithm 1

The SR1 algorithm for NNLS.

Step  1. start data

 Choose 𝐡⁰≥0, and the maximum iterative number 𝐦𝐚𝐱𝐢𝐭𝐞𝐫,

 Set 𝑙=0;

Step  2.

 Compute the inactive set by using the rule (9);

Step  3. (update the current solution)

 Renew current solution by (13), where using (16) to approximate

 the inverse of Hessian matrix and (17) to compute the stepsize;

Step  4.

 if the current result reaches the stop criterion then stop, the current

 solution is the final solution;

 else go to Step  2 and Step  3.