AN ALGORITHM FOR NONCONVEX PROGRAMMING

Abstract

The paper presents an algorithm to solve the most general mathematical programming problem: s.t. (g superscript i)(y) = or < 0, i = 1,2,. ..,m, Min. g(y), y = (y1,...,yn). The only restriction required is that the functions g superscript i, g be real valued. The general formulation allows for nonlinear or linear integer programming, mixed integer programming and general nonconvex continuous variable programming. The classical approaches have been essentially 'local' or 'neighborhood' techniques dependent on derivatives (or finite difference approximations to derivatives). They suffer from two serious difficulties which can be characterized as the 'dimensionality problem' and the problem of 'trapping at local optima.' Our central aim here is to present a new framework for reaching global optimum. The procedure involves two interconnected mechanisms, a method for structuring the search and a decision rule for selecting the course of the search.

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Document Details

Document Type
Technical Report
Publication Date
Sep 05, 1969
Accession Number
AD0697316

Entities

People

  • Andrew Whinston
  • G. Graves

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  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Classification
  • Computations
  • Computer Programming
  • Evolutionary Algorithms
  • Heuristic Methods
  • Integer Programming
  • Integrals
  • Mathematical Programming
  • Mathematics
  • Military Research
  • Nonconvex Programming
  • Numbers
  • Operations Research
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  • Mathematics

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  • Analytical Mechanics
  • Operations Research