Newton's Method for Generalized Equations.

Abstract

Newton's method is a well known and often applied technique for computing a zero of a nonlinear function. By using the theory of generalized equations, a Newton method is developed to solve problems arising in both mathematical programming and mathematical economics. Two results concerning the convergence and convergence rate of Newton's method are proved for generalized equations. Examples are given to emphasize the application of this method to generalized equations representing the non-linear programming problem and the nonlinear complementarity problem. Computational results of Newton's method applied to a nonlinear complementarity problem of Kojima, and an invariant capital stock problem of Hansen and Koopmans are both presented.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1979
Accession Number
ADA077096

Entities

People

  • Norman H. Josephy

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Business Administration
  • Computational Science
  • Computations
  • Computer Programming
  • Department Of Veterans Affairs
  • Equations
  • Linear Programming
  • Linear Systems
  • Mathematical Programming
  • Mathematics
  • New York
  • Nonlinear Programming
  • Nonlinear Systems
  • Operations Research
  • Sequences
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Operations Research