A Modified Newton Method for Unconstrained Minimization

Abstract

Newton's method has proved to be a very efficient method for solving strictly convex unconstrained minimization problems. For the nonconvex case, various modified Newton methods have been proposed. In this paper, a new modified Newton method is presented. The method is a line search method, utilizing the Cholesky factorization of a positive-definite portion of the Hessian matrix. The search direction is defined as a linear combination of a descent direction and a direction of negative curvature. Theoretical properties of the method are established and its behaviour is studied when applied to a set of test problems.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1989
Accession Number
ADA212752

Entities

People

  • Anders L. Forsgren
  • Philip Edward Gill
  • Walter Murray

Organizations

  • Stanford University

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Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Computations
  • Computer Programming
  • Eigenvalues
  • Equations
  • Integer Programming
  • Mathematical Programming
  • Mathematics
  • New York
  • Nonlinear Programming
  • Numerical Analysis
  • Operations Research
  • Optimization
  • Quadratic Programming
  • Sequences
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  • United States

Fields of Study

  • Mathematics

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  • Linear Algebra
  • Operations Research