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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.41  suppl.1 Bogotá Oct. 2007

 

An inexact Newton hybrid path-following algorithm for NLP

MIGUEL ARGÁEZ1, JAIME HERNÁNDEZ JR.2 & LETICIA VELÁZQUEZ2

1 Department of Mathematical Sciences, The University of Texas, El Paso, Texas, USA. E-mail: margaez@utep.edu
2 Department of Mathematical Sciences, The University of Texas, El Paso, Texas, USA.


Abstract

In this paper we present a hybrid path-following algorithm that generates inexact Newton steps suited for solving large scale and/or degenerate nonlinear programs. The algorithm uses as a central region a relaxed notion of the central path, called quasicentral path, a generalized augmented Lagrangian function, weighted proximity measures, and a linesearch within a trust region strategy. We apply a semi-iterative method for obtaining inexact Newton steps by using the conjugate gradient algorithm as an iterative procedure. We present a numerical comparison, and some promising results are reported.

Key words: Interior-point methods, trust region methods, linesearch technique, nonlinear programming, and conjugate gradient.


2000 Mathematics Subject Classification: Primary: 90C30. Secondary: 90C51, 90C06.

Resumen

En este artículo nosotros presentamos un algoritmo híbrido de seguimiento de camino que genera pasos inexactos de Newton para resolver problemas de gran escala o degenerados para programación no lineal. El algoritmo usa como una region de centralidad una noción mas débil que el bien conocido camino central, llamada camino quasi-central, una generalización de la función aumentada de Lagrange, medidas de aproximación pesadas, y una dirección de búsqueda dentro de una region de verdad. Nosotros aplicamos un método semi-iterativo para obtener direcciones inexactas del método de Newton usando el algoritmo del gradiente conjugado y presentamos una comparación numérica con resultados prometedores.

Palabras clave: Métodos de punto interior, Métodos de región verdadera, técnica de búsqueda de línea, programación nolinear y gradiente conjugado.


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