TRESNEI

TRESNEI is a MATLAB code for bound-constrained least-squares problems min f(x)= 0.5 ||F(x)||_2^2, l ≤ x ≤u, where : R^n --> R^m is a continuously differentiable function and l, u are defined n-dimensional lower and upper bounds such that -∞ ≤ l ≤ u ≤ ∞. Free and fixed variables are handled by setting corresponding components of l and u to be -∞ and ∞, or by setting them equal to each other. TRESNEI solves the nonlinear least-squares problem irrespective of its dimensions m and n. The algorithm implemented is a trust-region Gauss-Newton method which generates feasible iterates and relies on matrix factorization. The trust-region subproblem is solved by a dogleg strategy. The method is globally and fast locally convergent under standard assumptions. Various input/output options are provided, and we refer to the code itself for further documentation. TRESNEI covers the solution of small and zero residual bound-constrained nonlinear least-squares problems and handles the solution of systems of nonlinear equalities and inequalities. TRESNEI code has non-commercial purposes. We assume no responsibility for any errors that may exist in the provided routines. We welcome questions, comments, recommended changes and bug reports. If you use this code, the authors would appreciate your acknowledging having done so in the reports, publications, theses, etc., resulting from their use. Accompanying papers: [1] 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. [2] M.Macconi, B.Morini, M.Porcelli, "Trust-region quadratic methods for nonlinear systems of mixed equalities and inequalities", Applied Numerical Mathematics, (2009) 9:5, pp. 859-876. [3] M.Macconi, B.Morini, M.Porcelli, "A Gauss-Newton method for solving bound-constrained underdetermined nonlinear systems" , Optimization Methods and Software, (2009) 24:2, pp. 219-235. The file TRESNEI.zip contains: TRESNEI.m: the solver. Set1.zip: folder containing a driver program, test examples and the solver TRESNEI. Set2.zip: folder containing a driver program for CUTEr problems and the solver TRESNEI.