A PARAMETRIC PROGRAMMING SOLUTION TO THE VECTOR MAXIMUM PROBLEM, WITH APPLICATIONS TO DECISIONS UNDER UNCERTAINTY
Abstract
Some relationships between decision criteria for decision-making under uncertainty and risk are demonstrated. It is suggested that several criteria should be considered simultaneously so as to yield a vector maximum problem to be solved. It is shown that under certain conditions such a vector maximum problem can be reformulated as an equivalent parametric concave programming problem of the form: Maximize ab (x) + (1-a) c (x) subject to d (x) > or = 0 (i=1,...,m) for each fixed value of a in the unit interval, where fb and c are strictly concave functions of the decision vector x, the constraint functions are concave, and certain additonal regularity conditions are satisfied. A class of computational algorithms, based on maintaining a solution to the relevant Kuhn-Tucker conditions as a varies, is given for solving such programs. It is to be noted that the present algorithms also provide a deformation method for (nonparametric) concave programming. Illustrative examples are presented.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1965
- Accession Number
- AD0613670
Entities
People
- Arthur M. Geoffrion
Organizations
- University of California, Los Angeles