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An inexact Newton method combined with Hestenes multipliers' scheme for the solution of Karush-Kuhn-Tucker systems

APPLIED MATHEMATICS AND COMPUTATION 2005年第1期168卷 651-676页

作者： Bonettini, S Galligani, E Ruggiero, V Unv Modena & Reggio Emilia Dipartimento Matemat I-41100 Modena Italy Univ Ferrara Dipartmento Matemat I-44100 Ferrara Italy

In this work a Newton interior-point method for the solution of Karush-Kuhn-Tucker systems is presented. A crucial feature of this iterative method is the solution, at each iteration, of the inner subproblem. This subproblem is a linear-quadratic programming problem, that can solved approximately by an inner iterative method such as the Hestenes multipliers' method. A deep analysis on the choices of the parameters of the method (perturbation and damping parameters) has been done. The global convergence of the Newton interior-point method is proved when it is viewed as an inexact Newton method for the solution of nonlinear systems with restriction on the sign of some variables. The Newton interior-point method is numerically evaluated on large scale test problems arising from elliptic optimal control problems which show the effectiveness of the approach. (c) 2004 Elsevier Inc. All rights reserved.

关键词： Newton interior-point method inexact Newton method large scale nonlinear programming problems Hestenes multipliers' method elliptic control problems

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Some iterative methods for the solution of a symmetric indefinite KKT system

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2007年第1期38卷 3-25页

作者： Bonettini, Silvia Ruggiero, Valeria Univ Modena & Reggio Emilia Dipartimento Matemat Pura & Applicata I-41100 Modena Italy Univ Ferrara Dipartmento Matemat I-44100 Ferrara Italy

This paper is concerned with the numerical solution of a Karush-Kuhn-Tucker system. Such symmetric indefinite system arises when we solve a nonlinear programming problem by an Interior-Point (IP) approach. In this framework, we discuss the effectiveness of two inner iterative solvers: the method of multipliers and the preconditioned conjugate gradient method. We discuss the implementation details of these algorithms in an IP scheme and we report the results of a numerical comparison on a set of large scale test-problems arising from the discretization of elliptic control problems.

关键词： indefinite symmetric KKT system large scale nonlinear programming problems Interior Point method Hestenes' multipliers method preconditioned conjugate gradient method elliptic control problems

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Some iterative methods for the solution of a symmetric indefinite KKT system

Some iterative methods for the solution of a symmetric indef...

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Conference on High Performance Algorithms and Software for nonlinear Optimization

作者： Bonettini, Silvia Ruggiero, Valeria Univ Modena & Reggio Emilia Dipartimento Matemat Pura & Applicata I-41100 Modena Italy Univ Ferrara Dipartmento Matemat I-44100 Ferrara Italy

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