A Stable Theorem of the Alternative: An Extension of the Gordan Theorem.

Abstract

A theorem with a number of equivalent alternatives is proposed as an extension of the classical Gordan theorem of the alternative. The theorem can handle nonzero unrestricted variables which cannot be directly treated by ordinary theorems of the alternative. Like the Gordan theorem, the extended theorem has the stability feature that small perturbations in the data will not invalidate an alternative that is in force. The theorem has useful applications in establishing the boundedness and uniqueness of feasible points of polyhedral sets and of solutions to linear programming problems. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1981
Accession Number
ADA099347

Entities

People

  • Olvi L. Mangasarian

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computer Programming
  • Convex Sets
  • Engineering
  • Engineers
  • Heat Exchangers
  • Inequalities
  • Linear Programming
  • Materials
  • Mathematical Programming
  • Mathematics
  • Optimization
  • Perturbations
  • Real Numbers
  • Sequences
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.