AN EXPLICIT SOLUTION OF A SPECIAL CLASS OF LINEAR PROGRAMMING PROBLEMS

Abstract

The linear programs considered here are of the form: Maximize (c,x) (LP) subject to a = or < A x = or < b where A is of full row rank, and (LP) is feasible with bounded optimal solutions. The main result is an explicit representation of the general optimal solution of (LP), in terms of a generalized inverse of A. This explicit solution of (LP) - explicit in the sense that A superscript (-1) b is an explicit solution of A x = b - has obvious theoretical (and possibly computational) advantages over the well known iterative methods of linear programming. The results are illustrated by a simple example, and extensions to general linear programs are discussed.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1967
Accession Number
AD0663877

Entities

People

  • Abraham Charnes
  • Adi Ben-israel

Organizations

  • Northwestern University

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computer Programming
  • Construction
  • Contracts
  • Convex Programming
  • Equations
  • Interdisciplinary Science
  • Linear Programming
  • Mathematical Programming
  • Military Research
  • Operations Research
  • Security
  • Simplex Method
  • United States
  • United States Government
  • Universities
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Rocket Propulsion.