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首页> 外文期刊>Annali Dell Universita di Ferrara, Sezione VII. Scienze Matematiche >Block preconditioners for linear systems in interior point methods for convex constrained optimization
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Block preconditioners for linear systems in interior point methods for convex constrained optimization

机译：Block preconditioners for linear systems in interior point methods for convex constrained optimization

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Abstract In this paper, we address the preconditioned iterative solution of the saddle-point linear systems arising from the (regularized) Interior Point method applied to linear and quadratic convex programming problems, typically of large scale. Starting from the well-studied Constraint Preconditioner, we review a number of inexact variants with the aim to reduce the computational cost of the preconditioner application within the Krylov subspace solver of choice. In all cases we illustrate a spectral analysis showing the conditions under which a good clustering of the eigenvalues of the preconditioned matrix can be obtained, which foreshadows (at least in case PCG/MINRES Krylov solvers are used), a fast convergence of the iterative method. Results on a set of large size optimization problems confirm that the Inexact variants of the Constraint Preconditioner can yield efficient solution methods.

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