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

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...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 168; no. 1; pp. 651 - 676
Main Authors: Bonettini, Silvia, Galligani, Emanuele, Ruggiero, Valeria
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.09.2005
Elsevier
Subjects:
Calculus of variations and optimal control
Elliptic control problems
Exact sciences and technology
Global analysis, analysis on manifolds
Hestenes multipliers’ method
Inexact Newton method
Large scale nonlinear programming problems
Mathematical analysis
Mathematics
Newton interior-point method
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Elliptic control problems
Newton interior-point method
Inexact Newton method
Large scale nonlinear programming problems
Hestenes multipliers’ method
Damping
Hestenes method
Interior point method
Iterative method
Linear programming
Non linear programming
Quadratic programming
Non linear system
Convergence
Perturbation method
Numerical analysis
Applied mathematics
Perturbation techniques
Hestenes multipliers' method
Multiplier
Large scale
Newton method
ISSN:0096-3003, 1873-5649
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2004.09.018