Title:
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On geometrical properties of preconditioners in IPMs for classes of block-angular problems
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Author:
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Castro Pérez, Jordi; Nasini, Stefano
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Other authors:
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Universitat Politècnica de Catalunya. Departament d'Estadística i Investigació Operativa; Universitat Politècnica de Catalunya. GNOM - Grup d'Optimització Numèrica i Modelització |
Abstract:
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J. Castro, S. Nasini, On geometrical properties of preconditioners in IPMs for classes of block-angular problems, Research Report DR 2016/03, Dept. of Statistics and Operations Research, Universitat Politècnica de Catalunya, 2016. |
Abstract:
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One of the most efficient interior-point methods for some classes of block-angular structured problems
solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for,
respectively, the block and linking constraints. In this work we show that the choice of a good preconditioner depends on geometrical properties of the constraints structure. In particular, it is seen that the principal angles between the subspaces generated by the diagonal blocks and the linking constraints can be used to estimate ex-ante the efficiency of the preconditioner. Numerical validation is provided with some generated optimization problems. An application to the solution of multicommodity network flow problems with nodal capacities and equal flows of up to 127 million of
variables and up to 7.5 million of constraints is also presented |
Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització -interior-point methods -structured problems -preconditioned conjugate gradient -principal angles -large-scale optimization -Classificació AMS::90 Operations research, mathematical programming |
Rights:
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http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Document type:
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Article - Draft Report |
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