PROGRAMMING UNDER UNCERTAINTY: THE EQUIVALENT CONVEX PROGRAM

Abstract

This paper is an attempt to describe and characterize the equivalent convex program of a two-stage linear program under uncertainty. The study has been divided into two parts. In the first one, we examine the properties of the solution set of the problem and derive explicit expressions for some particular cases. The second section is devoted to the derivation of the objective function of the equivalent convex program. We show that it is convex and continuous. We also give a necessary condition for its differentiability and establish necessary and sufficient conditions for the solvability of the problem. Finally, we give the equivalent convex program of certain classes of programming under uncertainty problems, i.e. when the constraints and the probability space have particular structures.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1965
Accession Number
AD0612896

Entities

People

  • Roger J-B Wets

Organizations

  • Boeing

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Applied Mathematics
  • Computer Programming
  • Convex Programming
  • Convex Sets
  • Determinants (Mathematics)
  • Equations
  • Identities
  • Inequalities
  • Linear Programming
  • Mathematics
  • Operations Research
  • Probability
  • Random Variables
  • Standards
  • Topology

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space