PROPERTIES OF A GENERALIZED INVERSE WITH APPLICATIONS TO LINEAR PROGRAMMING THEORY

Abstract

In the first five sections of this paper various properties of a Rao generalized inverse of a matrix are established. A method of computing such an inverse is also given. In order to illustrate the differences between the Rao and other generalized inverses, a survey of results on Penrose-Moore inverses is included. The last three sections are devoted to showing how a generalized inverse can be used in the theoretical development of the simplex and modified simplex methods of linear programming. In particular, it is shown that the fundamental equations and iteration formulas of these methods can be derived using matrix notation without requiring the assumption that the linear programming problem has no redundant constraints.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1965
Accession Number
AD0629384

Entities

People

  • Abraham Charnes
  • Michael J. L. Kirby

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Abstracts
  • Algebra
  • Algorithms
  • Computations
  • Computer Programming
  • Consistency
  • Electrical Networks
  • Equations
  • Identities
  • Iterations
  • Linear Algebra
  • Linear Programming
  • Networks
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  • Simplex Method
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Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Linear Algebra