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

^*Corresponding author for this work

Industrial Engineering and Management Sciences

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

210 Scopus citations

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 (US)
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
State	Published - 2003

Keywords

Convergence theory
Filter methods
Nonlinear optimization
Sequential quadratic programming

ASJC Scopus subject areas

Software
Theoretical Computer Science

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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.",

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author = "Roger Fletcher and Gould, {Nicholas I M} and Sven Leyffer and Toint, {Philippe L.} and Andreas W{\"a}chter",

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AU - Gould, Nicholas I M

AU - Leyffer, Sven

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AU - Wächter, Andreas

PY - 2003

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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.

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