Accession Number : AD0668323

Title :   AN ALGORITHM FOR DIFFERENTIABLE CONVEX FUNCTIONAL PROGRAMMING WITH EXAMPLES AND APPLICATIONS TO LINEAR PROGRAMMING UNDER UNCERTAINTY.

Descriptive Note : Research rept.,

Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP

Personal Author(s) : Jagannathan,R.

Report Date : AUG 1967

Pagination or Media Count : 47

Abstract : The literature pertaining to linear programming under uncertainty is characterized by three major approaches, (i) Stochastic linear programming, (ii) chance constrained programming and (iii) Two-stage (in general m-stage) linear programming under uncertainty. These approaches offer a rich array of potential application possibilities provided algorithms can be made available to obtain solutions for any of the formulations that might be achieved. The present paper is directed to a study of some of the algorithmic possibilities with special reference to linear programming under uncertainty. More generally in Section 3 of this paper, a computational algorithm is developed for solving any convex programming problem with linear constraints when the criterion function has continuous derivatives. In Sections 4, 5, and 6 the applicability of the proposed procedure for solving a two-stage LP Model under three sets of assumptions regarding the stochastic nature of the defining parameters (A, B, c) is discussed. As illustrative examples, the capital budgeting and Portfolio Selection Models are considered in some detail. (Author)

Descriptors :   (*LINEAR PROGRAMMING, *UNCERTAINTY), PROBLEM SOLVING, DECISION THEORY, PROBABILITY, BUDGETS, FUNCTIONS(MATHEMATICS), FLOW CHARTING, OPTIMIZATION, MANAGEMENT PLANNING AND CONTROL, MATHEMATICAL PROGRAMMING, MATHEMATICAL MODELS, ITERATIONS, ALGORITHMS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE