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

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

Résultats de recherche: Papier de travailArticle de travail

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, 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.
langueAnglais
EditeurRutherford Appleton Laboratory
Nombre de pages43
VolumeRAL-TR-2014-001
étatPublié - 2 janv. 2014

Empreinte digitale

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

mots-clés

    Citer ceci

    Curtis, Frank ; Gould, N. I. M. ; Robinson, Daniel ; Toint, Ph. / An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization using a Squared-Violation Feasibility Measure. Rutherford Appleton Laboratory, 2014.
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    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.",
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    An Interior-Point Trust-Funnel Algorithm for Nonlinear Optimization using a Squared-Violation Feasibility Measure. / Curtis, Frank; Gould, N. I. M.; Robinson, Daniel; Toint, Ph.

    Rutherford Appleton Laboratory, 2014.

    Résultats de recherche: Papier de travailArticle de travail

    TY - UNPB

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    AU - Gould,N. I. M.

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    AU - Toint,Ph

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    N2 - 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.

    AB - 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.

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