@techreport{8b8d3455a1d241c7b708e14117912dfc,
title = "An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization using a Squared-Violation Feasibility Measure",
abstract = "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.",
keywords = "Nonlinear optimization, numerical methods, convergence theory",
author = "Frank Curtis and Gould, {N. I. M.} and Daniel Robinson and Ph Toint",
year = "2014",
month = jan,
day = "2",
language = "English",
volume = "RAL-TR-2014-001",
publisher = "Rutherford Appleton Laboratory",
type = "WorkingPaper",
institution = "Rutherford Appleton Laboratory",
}