THEORY OF LAGRANGE MULTIPLIERS FOR CONSTRAINED OPTIMIZATION PROBLEMS

Abstract

The paper treats an extension of one version of the classical Lagrange multiplier rule as applied to nonlinear programming problems. For a given problem, an auxiliary problem is defined and its properties are studied under various assumptions. In particular, when the given problem has a strictly convex objective function and concave constraints it is shown that the auxiliary problem is one of maximizing a concave differentiable function over an open set subject only to nonnegativity conditions. Some applications of this theory are presented only with the connection between the auxiliary problem and a 'dual' of the given problem.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1967
Accession Number
AD0658068

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People

  • James E. Falk

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Calculus Of Variations
  • Computer Programming
  • Convex Sets
  • Dynamic Programming
  • Evolutionary Algorithms
  • Inequalities
  • Lagrangian Functions
  • Linear Programming
  • Mathematical Programming
  • Mathematics
  • Nonlinear Programming
  • Operations Research
  • Optimization
  • Sequences
  • Theorems

Fields of Study

  • Mathematics

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  • Operations Research