Interior point and newton methods in solving high dimensional flow distribution problems for pipe networks

Статья конференции

Khamisov O.O., Stennikov V.A.

Журнал: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

11th International Conference on Learning and Intelligent Optimization, LION 2017

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol.10556 LNCS. P.139-149.

DOI: 10.1007/978-3-319-69404-7_10

ISBN: 9783319694030

2017

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. © Springer International Publishing AG 2017.

Библиографическая ссылка

Khamisov O.O., Stennikov V.A. Interior point and newton methods in solving high dimensional flow distribution problems for pipe networks // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol.10556 LNCS. 2017. P.139-149. ISBN (print): 9783319694030. DOI: 10.1007/978-3-319-69404-7_10

convex optimization