Software
This Matlab code provides the implementation of several algorithms, including two new effective ones, to solve the following problem: Given a (sparse) nonnegative matrix X(mxn) and a factorization rank r, compute W(mxr) and H(rxn) such that ||X - max(WH,0)||F2 is minimized.
BFO (Brute-Force Optimizer) an open-source direct-search derivative-free MATLAB solver for bound-constrained mathematical optimization problems.
M. Porcelli, Ph. L. Toint, BFO, a trainable derivative-free Brute Force Optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables, ACM Transactions on Mathematical Software 44:1 (2017), Article 6, 25 pages.
TRESNEI (Trust-REgion Solver for systems of Nonlinear Equalities and Inequalities) a Newton trust-region based method for solving systems of equalities and inequalities (MATLAB).
B.Morini, M.Porcelli, "TRESNEI, a Matlab trust-region solver for systems of nonlinear equalities and inequalities, Computational Optimization and Applications, (2012) 51:1, pp. 27-49.
barzilaiborwein is a Riemannian Barzilai-Borwein method for optimization problems on manifolds.
The MATLAB code is included in the Manopt library
B. Iannazzo, M. Porcelli, The Riemannian Barzilai-Borwein method with nonmonotone line-search and the matrix geometric mean computation, IMA Journal of Numerical Analysis, 38:1 (2018), pp. 495-517.
L2RT is a Fortran 95 package (part of the GALAHAD library) which approximately solves a regularized least l2-norm minimization problem. The implemented algorithm is based on the works [Cartis, Gould, Toint, BIT 2009] and [Bellavia, Cartis, Gould, Morini, Toint, SINUM 2010].
NOSA is a finite element code developed by the Mechanics of Materials and Structures Laboratory of ISTI-CNR with the aim of testing new constitutive models for materials, checking the algorithm used for integrating the equations of the motion, as well as other numerical techniques for solving structural engineering problems. NOSA can be used to study the static and dynamic behaviour of masonry buildings of historic and architectural interest and model the effectiveness of strengthening operations.
M. Porcelli, V. Binante, M. Girardi, C. Padovani, G. Pasquinelli, A solution procedure for constrained eigenvalue problems and its application within the structural finite element code NOSA-ITACA , CALCOLO, 52:2 (2015), pp. 167-186.