PROPER EFFICIENCY AND THE THEORY OF VECTOR MAXIMIZATION

Abstract

The concept of efficiency in problems with multiple criterion functions--sometimes under an alias such as 'admissibility' or 'Pareto optimality'--has long played an important role in economics, game theory, statistical decision theory, and in all optimal decision problems with noncomparable criteria. Here we propose a slightly restricted definition of efficiency that eliminates efficient points of a certain anomalous nature. This new definition, which we call proper efficiency, is related in spirit to the notion of 'proper' efficiency introduced by Kuhn and Tucker in their celebrated paper of 1950; but the present definition avoids certain drawbacks inherent in the earlier one. A comprehensive theory of vector maximization is constructed using the new definition, with and without various constraint qualification, convexity, and differentiability assumptions. The theory includes as a special case the standard theory of nonlinear programming.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1967
Accession Number
AD0659989

Entities

People

  • Arthur M. Geoffrion

Organizations

  • University of California, Los Angeles

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Air Force
  • California
  • Classification
  • Computer Programming
  • Convex Sets
  • Decision Theory
  • Economics
  • Efficiency
  • Game Theory
  • Military Research
  • Nonlinear Programming
  • Parametric Programming
  • Qualifications
  • Security
  • Statistical Decision Theory
  • Theorems
  • United States

Fields of Study

  • Economics
  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Statistical inference.
  • Systems Analysis and Design