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hom4msys.m  (Newly updated: March, 2019) Matlab code implementing a homotopy method for multilinear systems with M-tensors. Examples for testing this code: msysexamples.m

TenEig: A Matlab software package for computing tensor eigenvalues and eigenvectors.  Download:  here.

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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