Department of Mathematics and Statistics,
Arizona State University
Thursday,
April 22, 2004, 12:15 p.m. in GWC Room 110
Department of Mathematics, University of Modena, Italy
Interior-Point Methods as Inexact Newton Methods for Nonlinear Programs
Abstract
In this work we consider the solution of constrained nonlinear optimization problem by the interior point method. It is possible to view such a method as an inexact Newton method for Karush-Kuhn-Tucker systems that arise from optimality conditions of the optimization problem. This permits to show the convergence of the method even if the linear system (that has to be solved at each step of the method) is solved approximately, for instance by means of an inner iterative method such as Hestenes multipliers method or a preconditioned conjugate gradient method. An approximate solution is necessary when the iterate is far from the solution and when the size of the optimization problem is large. This approach is very efficient for the solution of large scale optimization problem arising from distributed or boundary elliptic control problem. Furthermore, it is possible to introduce, and show the convergence, of a nonmonotone inexact Newton method and then of a nonmonotone interior point method for nonlinear programs. Numerical experiments on elliptic control problems show the behaviour of this nonmonotone approach.
For further information please contact:
mittelmann@asu.edu