Two popular methods for unconstrained
minimization are: Trust Region
methods and Quasi-Newton methods.
Region Subproblems consist in minimizing a quadratic function
subject to a quadratic constraint. This
contains programs for solving the trust region subproblem. This routine
is in MATLAB. It uses the MATLAB eigs function, i.e.,
it finds the smallest eigenvalue using the Lanczos algorithm.
This program can solve large sparse problems very quickly. The research
report is available.
Also available are two related research reports: Indefinite
trust region subproblems provide characterizations of
optimality and relations to perturbed eigenvalue problems for
the case where both the objective and constraint can be indefinite;