An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization

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

Résultats de recherche: Contribution à un journal/une revueArticle

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Résumé

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 of being able to solve 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 with matrix-free methods so that derivative matrices need not be formed or factorized so long as matrix-vector products with them can be performed; (ii) the subproblems may be solved approximately in all iterations; (iii) in certain situations, the computed search directions represent inexact sequential quadratic optimization steps, which may be desirable for fast local convergence; (iv) criticality measures for feasibility and optimality aid in determining whether only a subset of computations need to be performed during a given iteration; and (v) no merit function or filter is needed to ensure global convergence.

langue originaleAnglais
Pages (de - à)73-134
Nombre de pages62
journalMathematical Programming
Volume161
Numéro de publication1-2
Les DOIs
étatPublié - janv. 2017

Empreinte digitale

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

Citer ceci

Curtis, Frank ; Gould, N. I. M. ; Robinson, Daniel ; Toint, Ph. / An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization. Dans: Mathematical Programming. 2017 ; Vol 161, Numéro 1-2. p. 73-134.
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An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization. / Curtis, Frank; Gould, N. I. M.; Robinson, Daniel; Toint, Ph.

Dans: Mathematical Programming, Vol 161, Numéro 1-2, 01.2017, p. 73-134.

Résultats de recherche: Contribution à un journal/une revueArticle

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