AN ALGORITHM FOR DIFFERENTIABLE CONVEX FUNCTIONAL PROGRAMMING WITH EXAMPLES AND APPLICATIONS TO LINEAR PROGRAMMING UNDER UNCERTAINTY.
CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
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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
- Operations Research