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Jordi Castro(jordi.castroupc.edu) Abstract: One of the most efficient interiorpoint methods for some classes of primal blockangular 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 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 blockangular 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 stateoftheart commercial solvers. Keywords: interiorpoint methods · primal blockangular problems · multicommodity network flows · preconditioned conjugate gradient · regularizations · largescale computational optimization Category 1: Linear, Cone and Semidefinite Programming Category 2: Nonlinear Optimization (Quadratic Programming ) Citation: J. Castro, J. Cuesta, Quadratic regularizations in an interiorpoint method for primal blockangular problems, Research Report DR 2008/07, Dept. of Statistics and Operations Research, Universitat Politècnica de Catalunya, 2008. Download: [PDF] Entry Submitted: 09/02/2008 Modify/Update this entry  
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