Solving structured nonlinear least-squares and
nonlinear feasibility problems with expensive functions
M. Kaiser, K. Klamroth, A. Thekale, Ph. L. Toint
Report NAXYS-07-2010
We present an algorithm for nonlinear least-squares and nonlinear feasibility
problems, i.e. for systems of nonlinear equations and nonlinear inequalities,
which depend on the outcome of expensive functions for which derivatives are
assumed to be unavailable. Our algorithm combines derivative-free techniques
with filter trust-region methods to keep the number of expensive function
evaluations low and to obtain a robust method. Under adequate assumptions, we
show global convergence to a feasible point. Numerical results indicate a
significant reduction in function evaluations compared to other derivative
based and derivative-free solvers for nonlinear feasibility problems.