The Use of Linear Programming for the Solution of Sparse Sets of Nonlinear Equations

I. S. Duff; J. Nocedal; J. K. Reid

doi:10.1137/0908024

The Use of Linear Programming for the Solution of Sparse Sets of Nonlinear Equations

I. S. Duff, J. Nocedal, J. K. Reid

Industrial Engineering and Management Sciences

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

Abstract

In this paper we propose a trust region algorithm for solving sparse sets of nonlinear equations. It is based on minimizing the $l_1 $-norm of the linearized residual vector within an $l_\infty $-norm trust region, thereby permitting linear programming techniques to be easily applied. The new algorithm has sparsity advantages over the Levenberg-Marquardt algorithm.

Original language	English
Pages (from-to)	99-108
Journal	SIAM Journal on Scientific Computing
Volume	8
DOIs	https://doi.org/10.1137/0908024
State	Published - 1987

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title = "The Use of Linear Programming for the Solution of Sparse Sets of Nonlinear Equations",

abstract = "In this paper we propose a trust region algorithm for solving sparse sets of nonlinear equations. It is based on minimizing the $l_1 $-norm of the linearized residual vector within an $l_\infty $-norm trust region, thereby permitting linear programming techniques to be easily applied. The new algorithm has sparsity advantages over the Levenberg-Marquardt algorithm.",

author = "Duff, {I. S.} and J. Nocedal and Reid, {J. K.}",

year = "1987",

doi = "10.1137/0908024",

language = "English",

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journal = "SIAM Journal on Scientific Computing",

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T1 - The Use of Linear Programming for the Solution of Sparse Sets of Nonlinear Equations

AU - Duff, I. S.

AU - Nocedal, J.

AU - Reid, J. K.

PY - 1987

Y1 - 1987

N2 - In this paper we propose a trust region algorithm for solving sparse sets of nonlinear equations. It is based on minimizing the $l_1 $-norm of the linearized residual vector within an $l_\infty $-norm trust region, thereby permitting linear programming techniques to be easily applied. The new algorithm has sparsity advantages over the Levenberg-Marquardt algorithm.

AB - In this paper we propose a trust region algorithm for solving sparse sets of nonlinear equations. It is based on minimizing the $l_1 $-norm of the linearized residual vector within an $l_\infty $-norm trust region, thereby permitting linear programming techniques to be easily applied. The new algorithm has sparsity advantages over the Levenberg-Marquardt algorithm.

U2 - 10.1137/0908024

DO - 10.1137/0908024

M3 - Article

SN - 1064-8275

VL - 8

SP - 99

EP - 108

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

ER -

The Use of Linear Programming for the Solution of Sparse Sets of Nonlinear Equations

Abstract

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