THE LAGRANGE MULTIPLIER, A HEURISTIC PRESENTATION

Abstract

Many problems in operations research require the maximization or minimization of a suitable payoff function subject to various constraints. Lagrange multipliers are classically used for this type of problem, however, the treatment given this technique by most texts requires that the payoff and constraint functions be at least differentiable at the extremizing point. This paper shows that the Lagrange multiplier concept can be independent of differentiability or even continuity of the functions involved. It also gives the reader a geometric insight into the workings of the multiplier. Simplifications possible, if the functions involved are homogeneous, are displayed. The treatment is heuristic rather than formally rigorous.

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Document Details

Document Type
Technical Report
Publication Date
Oct 31, 1966
Accession Number
AD0643740

Entities

People

  • W. R. Nunn

Organizations

  • Center for Naval Analyses

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Classification
  • Computers
  • Continuity
  • Contracts
  • Differential Equations
  • Equations
  • Homogeneity
  • Inequalities
  • Inspection
  • Military Research
  • Notation
  • Numbers
  • Numerical Integration
  • Operations Research
  • Partial Differential Equations
  • Test And Evaluation

Readers

  • Calculus or Mathematical Analysis
  • Systems Analysis and Design