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An Importance Sampling Approach to the Estimation of Algorithm Performance in Automated Algorithm Design Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Interior Point and Newton Methods in Solving High Dimensional Flow Distribution Problems for Pipe Networks

Authors : Oleg O. Khamisov, Valery A. Stennikov

Published in: Learning and Intelligent Optimization

Publisher: Springer International Publishing

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Abstract

In this paper optimal flow distribution problem in pipe network is considered. The investigated problem is a convex sparse optimization problem with linear equality and inequality constrains. Newton method is used for problem with equality constrains only and obtains an approximate solution, which may not satisfy inequality constraints. Then Dikin Interior Point Method starts from the approximate solution and finds an optimal one. For problems of high dimension sparse matrix methods, namely Conjugate Gradient and Cholesky method with nested dissection, are applied. Since Dikin Interior Point Method works much slower then Newton Method on the matrices of big size, such approach allows us to obtain good starting point for this method by using comparatively fast Newton Method. Results of numerical experiments are presented.

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Metadata
Title
Interior Point and Newton Methods in Solving High Dimensional Flow Distribution Problems for Pipe Networks
Authors
Oleg O. Khamisov
Valery A. Stennikov
Copyright Year
2017
Book
Learning and Intelligent Optimization

Print ISBN: 978-3-319-69403-0

Electronic ISBN: 978-3-319-69404-7

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-69404-7_10

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