An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization
F. Curtis, N. Gould, D. Robinson and Ph. L. Toint
Report NAXYS-02-2014 20 February 2014
We present an interior-point trust-funnel algorithm for solving large-scale
nonlinear optimization problems. The method is based on an approach
proposed by Gould and Toint (Math. Prog., 122(1):155-196, 2010) that
focused on solving equality constrained problems. Our method is similar in
that it achieves global convergence guarantees by combining a trust-region
methodology with a funnel mechanism, but has the additional capability that
it solves problems with both equality and inequality constraints. The
prominent features of our algorithm are that (i) the subproblems that define
each search direction may be solved approximately, (ii) criticality measures
for feasibility and optimality aid in determining which subset of
computations will be performed during each iteration, (iii) no merit
function or filter is used, (iv) inexact sequential quadratic optimization
steps may be utilized when advantageous, and (v) it may be implemented
matrix-free so that derivative matrices need not be formed or factorized so
long as matrix-vector products with them can be performed.