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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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 constraint structure. In particular, 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 64 million variables and up to 7.9 million constraints is also presented. These computational results also show that predictor-corrector directions combined with iterative system solves can be a competitive option for large instances. |
Abstract:
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Peer Reviewed |
Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa -Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming |
Rights:
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Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Document type:
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Article - Submitted version Article |
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