PROPER EFFICIENCY AND THE THEORY OF VECTOR MAXIMIZATION
CALIFORNIA UNIV LOS ANGELES WESTERN MANAGEMENT SCIENCE INST
Pagination or Media Count:
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.
- Operations Research