On the Formulation and Theory of the Newton Interior-Point Method for Nonlinear Programming

Abstract

In this work we first study in detail the formulation of the primal-dual interior- point method for linear programming. We show that, contrary to popular belief, it cannot be viewed as the damped Newton method applied to the Karush-Kuhn-Tucker conditions for the logarithmic barrier function problem. Next we extend the formulation to general nonlinear programming, and then validate this extension by demonstrating that this algorithm can be implemented so that it is locally and Q-quadratically convergent under only the standard Newton's method assumptions. We also establish a global convergence theory for this algorithm and include promising numerical experimentation.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1995
Accession Number
ADA453865

Entities

People

  • A. S. El-bakry
  • Richard A. Tapia
  • T. Tsuchiya
  • Yinglong Zhang

Organizations

  • Rice University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Applied Mathematics
  • Computer Programming
  • Information Operations
  • Interdisciplinary Science
  • Linear Programming
  • Mathematical Programming
  • Mathematics
  • Nonlinear Programming
  • Operations Research
  • Systems Science

Fields of Study

  • Mathematics

Readers

  • Operations Research