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ANMS.m (Adaptive Nelder-Mead Simplex
algorithm for unconstrained optimization).
This
Matlab code implements the Nelder-Mead
simplex method using the adaptive parameters proposed in: Fuchang Gao and Lixing Han, Implementing the Nelder-Mead simplex algorithm with adaptive parameters,
Computational
Optimization and Applications,
Vol. 51, No. 1, 2012, pp. 259-277. The code also uses a relatively large
initial simplex (The initial simplex used in the numerical experiments in
the above paper is small in order to compare ANMS and FMINSEARCH).
Numerical tests show that it can outperform the standard implementation of
the Nelder-Mead method for high dimensional
problems (say, n>=10) and for noisy problems. REMARK: You may
consider to change the initial simplex based on
your own need.
APBB2.m (Alternating Projected Barzilai-Borwein
method for NMF).
This Matlab code implements an
alternating projected Barzilai-Borwein method for
solving nonnegative matrix factorization problems. This code calls
PBBNLS2.m (which is included), a code that implements a projected Barzilai-Borwein method for solving nonnegative linear
least squares problems in matrix form. For more details, please see: Lixing
Han, Michael Neumann, and Upendra Prasad,
Alternating projected Barzilai-Borwein methods
for nonnegative matrix factorization, Electronic Transactions on Numerical Analysis, Vol. 36, 2009-2010, pp. 54-82.
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