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

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Abstract

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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Authors and Affiliations

  1. Department of Statistics and Operations Research, Universitat Politècnica de Catalunya, Jordi Girona 1–3, 08034, Barcelona, Catalonia, Spain

    Jordi Castro

  2. Statistics and Operations Research unit, Department of Chemical Engineering, Universitat Rovira i Virgili, Avda. Països Catalans 26, 43007, Tarragona, Catalonia, Spain

    Jordi Cuesta

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  1. Jordi Castro
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  2. Jordi Cuesta
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Correspondence to Jordi Castro.

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Castro, J., Cuesta, J. Quadratic regularizations in an interior-point method for primal block-angular problems. Math. Program. 130, 415–445 (2011). https://doi.org/10.1007/s10107-010-0341-2

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  • DOI: https://doi.org/10.1007/s10107-010-0341-2

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