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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.

MSC:
 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
Software:
CUTEr; HOPDM; HSL; NETLIB LP Test Set; nlpy; OOQP; PCx; PDCO; SifDec
Full Text:
References:
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