CRPC-TR99793-S						September 1999

Title: The Sphere of Convergence of Newton's Method on Two Equivalent 
Systems from Nonlinear Programming

Authors: Maria Cristina Villalobos, Richard A. Tapia, and Yin Zhang

Submitted November 1999

Abstract:
We study a local feature of a Newton logarithmic barrier function method
and a Newton primal-dual interior-point method. In particular, we study
the radius of the sphere of convergence of Newton's method on two
equivalent systems associated with the two aforementioned interior-point
methods for nondegenerate problems in inequality contrained optimization
problems. Our theoretical and numerical results are clearly in favor of
using Newton primal-dual methods for solving the optimization problem.
This work is an extension of the authors' earlier work [10] on linear
programming problems.

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Maria Cristina Villalobos
cristina@caam.rice.edu
Department of Computational and Applied Mathematics
Rice University

Richard Tapia
rat@caam.rice.edu
Department of Computational and Applied Mathematics
Rice University

Yin Zhang
zhang@caam.rice.edu
Department of Computational and Applied Mathematics
Rice Universityz