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A primal-dual regularized interior-point method for convex quadratic programs. (English) Zbl 1279.90193
Summary: 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 termed exact to emphasize that, although the problems are regularized, the algorithm recovers a solution of the original problem, for appropriate values of the regularization parameters.

90C51 Interior-point methods
90C20 Quadratic programming
90C05 Linear programming
90C06 Large-scale problems in mathematical programming
90C25 Convex programming
65F22 Ill-posedness and regularization problems in numerical linear algebra
65F50 Computational methods for sparse matrices
Full Text: DOI
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