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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Bibliographic Details
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
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0368-4245
0036-1399
2168-3484
1095-712X
DOI:10.1137/0109040