Accelerating the Cutting Plane Method for Nonlinear Programming

The "cutting plane" method of Kelley for nonlinear programming problems applies linear programming, through a sequence of local linearizations, to the problem of minimizing a convex function of real variables subject to linear inequality constraints. A procedure is presented here for impro...

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Published inJournal of the Society for Industrial and Applied Mathematics Vol. 9; no. 3; pp. 481 - 488
Main Author Wolfe, Philip
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.09.1961
Subjects
Algorithms
Geometric planes
Inequality
Linear programming
Mathematical functions
Mathematical procedures
Nonlinear programming
Perceptron convergence procedure
Variables
Online AccessGet full text
ISSN0368-4245
0036-1399
2168-3484
1095-712X
DOI10.1137/0109040

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Abstract The "cutting plane" method of Kelley for nonlinear programming problems applies linear programming, through a sequence of local linearizations, to the problem of minimizing a convex function of real variables subject to linear inequality constraints. A procedure is presented here for improving the constructed linearizations which may considerably accelerate the convergence of the process. In the case of a quadratic objective function satisfying certain mild conditions this improvement yields a finite algorithm.
AbstractList The "cutting plane" method of Kelley for nonlinear programming problems applies linear programming, through a sequence of local linearizations, to the problem of minimizing a convex function of real variables subject to linear inequality constraints. A procedure is presented here for improving the constructed linearizations which may considerably accelerate the convergence of the process. In the case of a quadratic objective function satisfying certain mild conditions this improvement yields a finite algorithm.
Author Wolfe, Philip
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Cites_doi 10.1137/0108053
10.1145/368518.368542
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Copyright Copyright 1961 Society for Industrial and Applied Mathematics
[Copyright] © 1961 Society for Industrial and Applied Mathematics
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SubjectTerms Algorithms
Geometric planes
Inequality
Linear programming
Mathematical functions
Mathematical procedures
Nonlinear programming
Perceptron convergence procedure
Variables
Title Accelerating the Cutting Plane Method for Nonlinear Programming
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