Mathematical Programming Computation

, Volume 4, Issue 1, pp 71–107 | Cite as

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

Full Length Paper

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.

Mathematics Subject Classification (2000)

90C05 90C06 90C20 90C25 90C51 65F22 65F50 

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Copyright information

© Springer and Mathematical Optimization Society 2012

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada
  2. 2.GERAD, Department of Mathematics and Industrial EngineeringÉcole PolytechniqueMontréalCanada

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