A CONVEX APPROXIMANT METHOD FOR NON-CONVEX EXTENSIONS OF GEOMETRIC PROGRAMMING

Abstract

Many important problems of engineering and management are of a form which could be represented as geometric programs except that the functional to be minimized as well as the constraints are not confined to posynomials in that some of the coefficients are negative. This paper supplies a way for dealing with such negative terms by a constraint adjunction procedure which yields an associated approximating problem involving only polynomials which can, in turn, be transformed into a convex programming problem that has only one local (= global) optimum. The latter, which is called a convex approximant, has an associated dual. Recourse to the related duality theory then supplies guidance for improving the approximation along lines that are indicated in the paper.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 05, 1966
Accession Number
AD0633282

Entities

People

  • A. Charnes
  • W. W. Cooper

Organizations

  • Carnegie Institute of Technology

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Classification
  • Coefficients
  • Computer Programming
  • Contractors
  • Contracts
  • Convex Programming
  • Engineering
  • Geometric Programming
  • Linear Programming
  • Mathematical Programming
  • Military Research
  • Optimization
  • Production
  • Security
  • Systems Engineering

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.
  • Systems Analysis and Design