Global convergence of a class of trust region algorithms for optimization with simple bounds

Andy Conn; Nick Gould; Philippe Toint

Global convergence of a class of trust region algorithms for optimization with simple bounds

Andy Conn, Nick Gould, Philippe Toint

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

Abstract

This paper extends the known excellent global convergence properties of trust-region algorithms for unconstrained optimization to the case where bounds on the variables are present. Weak conditions on the accuracy of the Hessian approximations are considered. It is also shown that, when the strict complementarity condition holds, the proposed algorithms reduce to an unconstrained calculation after finitely many iterations, allowing a fast rate of convergence.

Original language	English
Pages (from-to)	430-460
Number of pages	31
Journal	SIAM Journal on Numerical Analysis
Volume	25
Issue number	182
Publication status	Published - 1988

1 Finished
1 Active

ADALGOPT: ADALGOPT - Advanced algorithms in nonlinear optimization
Sartenaer, A. & TOINT, P.
1/01/87 → …
Project: Research Axis
LANCELOT: LANCELOT, a package for the solution of large-scale nonlinear optimization problems
TOINT, P., Sartenaer, A., Gould, N. I. M. & Conn, A.
1/09/87 → 1/09/00
Project: Research

Cite this

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title = "Global convergence of a class of trust region algorithms for optimization with simple bounds",

abstract = "This paper extends the known excellent global convergence properties of trust-region algorithms for unconstrained optimization to the case where bounds on the variables are present. Weak conditions on the accuracy of the Hessian approximations are considered. It is also shown that, when the strict complementarity condition holds, the proposed algorithms reduce to an unconstrained calculation after finitely many iterations, allowing a fast rate of convergence.",

author = "Andy Conn and Nick Gould and Philippe Toint",

year = "1988",

language = "English",

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pages = "430--460",

journal = "SIAM Journal on Numerical Analysis",

issn = "1095-7170",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "182",

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AU - Conn, Andy

AU - Gould, Nick

AU - Toint, Philippe

PY - 1988

Y1 - 1988

N2 - This paper extends the known excellent global convergence properties of trust-region algorithms for unconstrained optimization to the case where bounds on the variables are present. Weak conditions on the accuracy of the Hessian approximations are considered. It is also shown that, when the strict complementarity condition holds, the proposed algorithms reduce to an unconstrained calculation after finitely many iterations, allowing a fast rate of convergence.

AB - This paper extends the known excellent global convergence properties of trust-region algorithms for unconstrained optimization to the case where bounds on the variables are present. Weak conditions on the accuracy of the Hessian approximations are considered. It is also shown that, when the strict complementarity condition holds, the proposed algorithms reduce to an unconstrained calculation after finitely many iterations, allowing a fast rate of convergence.

M3 - Article

SN - 1095-7170

VL - 25

SP - 430

EP - 460

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 182

ER -

Global convergence of a class of trust region algorithms for optimization with simple bounds

Abstract

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Projects

ADALGOPT: ADALGOPT - Advanced algorithms in nonlinear optimization

LANCELOT: LANCELOT, a package for the solution of large-scale nonlinear optimization problems

Cite this