A PARAMETRIC PROGRAMMING SOLUTION TO THE VECTOR MAXIMUM PROBLEM, WITH APPLICATIONS TO DECISIONS UNDER UNCERTAINTY

Abstract

This work begins with a study of individual decision-making under uncertainty. Several methods for circumventing uncertainty in the constraints are briefly reviewed, and several decision criteria for circumventing uncertainty in the objective function are discussed. Particular attention is devoted to the demonstration of certain relationships between these criteria. It is concluded that vector maximum reformulations of the problem play a prominent role in dealing with uncertainty in such decision problems. Two methods for transforming a vector maximum problem into an equivalent parametric programming problem are discussed. Existing computational methods for the latter problems are briefly surveyed. The principal contribution of this work is presented as a class of algorithms for solving parametric concave programming problems. This problem also subsumes the standard (non-parametric) concave programming problem when a feasible solution is known. Thus the present algorithms provide a deformation method of concave programming.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1965
Accession Number
AD0461480

Entities

People

  • Arthur M. Geoffrion

Organizations

  • Stanford University

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • Analytic Functions
  • Complex Variables
  • Computational Science
  • Computer Programming
  • Convex Sets
  • Linear Programming
  • Mathematical Analysis
  • Mathematical Programming
  • Numerical Analysis
  • Operations Research
  • Parametric Programming
  • Probability
  • Probability Distributions
  • Quadratic Programming
  • Random Variables
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Operations Research
  • Regression Analysis.
  • Systems Analysis and Design