An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization using a Squared-Violation Feasibility Measure

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, which is designed to solve problems with both
equality and inequality constraints, achieves global convergence
guarantees by combining a trust-region methodology with a funnel
mechanism. 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
computed 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. This variant
uses the square of the violation as a feasibility measure.