CONVERGENCE CONDITIONS FOR NONLINEAR PROGRAMMING ALGORITHMS

Abstract

Conditions which are necessary and sufficient for convergence of a nonlinear programming algorithm are stated. It is also shown that the convergence conditions can be easily applied to most programming algorithms. As examples, algorithms by Arrow, Hurwicz and Uzawa; Cauchy; Frank and Wolfe; and Newton-Raphson are proven to converge by direct application of the convergence conditions. Also the Topkis-Veinott convergence conditions for feasible direction algorithms are shown to be a special case of the conditions stated in this paper.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1968
Accession Number
AD0672928

Entities

People

  • W. I. Zangwill

Organizations

  • University of California, Berkeley

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  • Autonomy
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • California
  • Computer Programming
  • Computers
  • Continuity
  • Convergence
  • Difference Equations
  • Differential Equations
  • Digital Computers
  • Equations
  • Inequalities
  • Linear Programming
  • Military Research
  • Nonlinear Programming
  • Sequences
  • Simplex Method
  • United States

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  • Linear Algebra
  • Operations Research