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A primal–dual regularized interior-point method for convex quadratic programs

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Abstract

Interior-point methods in augmented form for linear and convex quadratic programming require the solution of a sequence of symmetric indefinite linear systems which are used to derive search directions. Safeguards are typically required in order to handle free variables or rank-deficient Jacobians. We propose a consistent framework and accompanying theoretical justification for regularizing these linear systems. Our approach can be interpreted as a simultaneous proximal-point regularization of the primal and dual problems. The regularization is termedexact to emphasize that, although the problems are regularized, the algorithm recovers a solution of the original problem, for appropriate values of the regularization parameters.

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Authors and Affiliations

  1. Department of Computer Science, University of British Columbia, Vancouver, BC, Canada

    M. P. Friedlander

  2. GERAD, Department of Mathematics and Industrial Engineering, École Polytechnique, Montréal, QC, Canada

    D. Orban

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  1. M. P. Friedlander
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  2. D. Orban
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Correspondence to M. P. Friedlander.

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Friedlander, M.P., Orban, D. A primal–dual regularized interior-point method for convex quadratic programs. Math. Prog. Comp. 4, 71–107 (2012). https://doi.org/10.1007/s12532-012-0035-2

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