Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming

Roger Fletcher; Nicholas I.M. Gould; Sven Leyffer; Philippe L. Toint; Andreas Wächter

doi:10.1137/S1052623499357258

Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming

Roger Fletcher, Nicholas I.M. Gould, Sven Leyffer, Philippe L. Toint, Andreas Wächter

Research output: Contribution to journal › Article › peer-review

230 Citations (Scopus)

Abstract

A trust-region SQP-filter algorithm of the type introduced by Fletcher and Leyffer [Math. Program., 91 (2002), pp. 239-269] that decomposes the step into its normal and tangential components allows for an approximate solution of the quadratic subproblem and incorporates the safeguarding tests described in Fletcher, Leyffer, and Toint [On the Global Convergence of an SLP-Filter Algorithm, Technical Report 98/13, Department of Mathematics, University of Namur, Namur, Belgium, 1998; On the Global Convergence of a Filter-SQP Algorithm, Technical Report 00/15, Department of Mathematics, University of Namur, Namur, Belgium, 2000] is considered. It is proved that, under reasonable conditions and for every possible choice of the starting point, the sequence of iterates has at least one first-order critical accumulation point.

Original language	English
Pages (from-to)	635-659
Number of pages	25
Journal	SIAM Journal on Optimization
Volume	13
Issue number	3
DOIs	https://doi.org/10.1137/S1052623499357258
Publication status	Published - 2003

Keywords

Convergence theory
Filter methods
Nonlinear optimization
Sequential quadratic programming

ASJC Scopus subject areas

Software
Theoretical Computer Science

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10.1137/S1052623499357258Licence: Other

Cite this

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title = "Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming",

abstract = "A trust-region SQP-filter algorithm of the type introduced by Fletcher and Leyffer [Math. Program., 91 (2002), pp. 239-269] that decomposes the step into its normal and tangential components allows for an approximate solution of the quadratic subproblem and incorporates the safeguarding tests described in Fletcher, Leyffer, and Toint [On the Global Convergence of an SLP-Filter Algorithm, Technical Report 98/13, Department of Mathematics, University of Namur, Namur, Belgium, 1998; On the Global Convergence of a Filter-SQP Algorithm, Technical Report 00/15, Department of Mathematics, University of Namur, Namur, Belgium, 2000] is considered. It is proved that, under reasonable conditions and for every possible choice of the starting point, the sequence of iterates has at least one first-order critical accumulation point.",

keywords = "Convergence theory, Filter methods, Nonlinear optimization, Sequential quadratic programming",

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T1 - Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming

AU - Fletcher, Roger

AU - Gould, Nicholas I.M.

AU - Leyffer, Sven

AU - Toint, Philippe L.

AU - Wächter, Andreas

PY - 2003

Y1 - 2003

N2 - A trust-region SQP-filter algorithm of the type introduced by Fletcher and Leyffer [Math. Program., 91 (2002), pp. 239-269] that decomposes the step into its normal and tangential components allows for an approximate solution of the quadratic subproblem and incorporates the safeguarding tests described in Fletcher, Leyffer, and Toint [On the Global Convergence of an SLP-Filter Algorithm, Technical Report 98/13, Department of Mathematics, University of Namur, Namur, Belgium, 1998; On the Global Convergence of a Filter-SQP Algorithm, Technical Report 00/15, Department of Mathematics, University of Namur, Namur, Belgium, 2000] is considered. It is proved that, under reasonable conditions and for every possible choice of the starting point, the sequence of iterates has at least one first-order critical accumulation point.

AB - A trust-region SQP-filter algorithm of the type introduced by Fletcher and Leyffer [Math. Program., 91 (2002), pp. 239-269] that decomposes the step into its normal and tangential components allows for an approximate solution of the quadratic subproblem and incorporates the safeguarding tests described in Fletcher, Leyffer, and Toint [On the Global Convergence of an SLP-Filter Algorithm, Technical Report 98/13, Department of Mathematics, University of Namur, Namur, Belgium, 1998; On the Global Convergence of a Filter-SQP Algorithm, Technical Report 00/15, Department of Mathematics, University of Namur, Namur, Belgium, 2000] is considered. It is proved that, under reasonable conditions and for every possible choice of the starting point, the sequence of iterates has at least one first-order critical accumulation point.

KW - Convergence theory

KW - Filter methods

KW - Nonlinear optimization

KW - Sequential quadratic programming

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DO - 10.1137/S1052623499357258

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Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming

Abstract

Keywords

ASJC Scopus subject areas

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