An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization

Frank Curtis, N. I. M. Gould, Daniel Robinson, Ph Toint

Research output: Research - peer-reviewArticle

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.
LanguageEnglish
Pages73-134
Number of pages43
JournalMathematical Programming
Volume161
Issue number1
StatePublished - Jan 2017

Fingerprint

Interior Point
Nonlinear Optimization
Matrix Derivative
Merit Function
Quadratic Optimization
Trust Region
Large-scale Optimization
Cross product
Matrix Product
Equality Constraints
Criticality
Inequality Constraints
Global Convergence
Nonlinear Problem
Optimality
Equality
Filter
Optimization Problem
Iteration
Subset

Keywords

  • Nonlinear optimization
  • numerical methods
  • convergence theory

Cite this

Curtis, F., Gould, N. I. M., Robinson, D., & Toint, P. (2017). An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization. Mathematical Programming, 161(1), 73-134.
Curtis, Frank ; Gould, N. I. M. ; Robinson, Daniel ; Toint, Ph. / An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization. In: Mathematical Programming. 2017 ; Vol. 161, No. 1. pp. 73-134
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Curtis, F, Gould, NIM, Robinson, D & Toint, P 2017, 'An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization' Mathematical Programming, vol 161, no. 1, pp. 73-134.

An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization. / Curtis, Frank; Gould, N. I. M.; Robinson, Daniel; Toint, Ph.

In: Mathematical Programming, Vol. 161, No. 1, 01.2017, p. 73-134.

Research output: Research - peer-reviewArticle

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