Quadratic regularizations in an interior-point method for primal block-angular problems

One of the most efficient interior-point methods for some classes of primal block-angular problems solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for, respectively, the block and linking constraints. Its efficiency depends on the spectra...

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Bibliographic Details
Published in:Mathematical programming Vol. 130; no. 2; pp. 415 - 445
Main Authors: Castro, Jordi, Cuesta, Jordi
Format: Journal Article Publication
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.12.2011
Springer
Springer Nature B.V
Subjects:
90 Operations research, mathematical programming
90C Mathematical programming
Algorithms
Applied sciences
Blocking
Calculus of Variations and Optimal Control; Optimization
Classificació AMS
Combinatorics
Computing time
Conjugate gradients
Exact sciences and technology
Flows in networks. Combinatorial problems
Full Length Paper
Investigació operativa
Linear programming
Matemàtiques i estadística
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Methods
Network management systems
Numerical Analysis
Operational research and scientific management
Operational research. Management science
Operations research
Optimització
Programació (Matemàtica)
Programming (Mathematics)
Regularization
Spectra
Studies
Theoretical
Àrees temàtiques de la UPC
Preconditioned conjugate gradient
Large-scale computational optimization
90C51
Multicommodity network flows
90C06
Interior-point methods
Primal block-angular problems
Regularizations
90C08
Barrier function
Spectral radius
Perron value
Matrix factorization
Modeling
Convex programming
Multicommodity flow problem
Cholesky method
Cholesky factorization
Conjugate gradient method
Network flow
Interior point method
Constrained optimization
Large scale
Preconditioning
Regularization
ISSN:0025-5610, 1436-4646
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Summary:One of the most efficient interior-point methods for some classes of primal block-angular problems solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for, respectively, the block and linking constraints. Its efficiency depends on the spectral radius—in [0,1)— of a certain matrix in the definition of the preconditioner. Spectral radius close to 1 degrade the performance of the approach. The purpose of this work is twofold. First, to show that a separable quadratic regularization term in the objective reduces the spectral radius, significantly improving the overall performance in some classes of instances. Second, to consider a regularization term which decreases with the barrier function, thus with no need for an extra parameter. Computational experience with some primal block-angular problems confirms the efficiency of the regularized approach. In particular, for some difficult problems, the solution time is reduced by a factor of two to ten by the regularization term, outperforming state-of-the-art commercial solvers.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-010-0341-2