Showing papers on "Concave function published in 1972"

Steepest Ascent for Large Scale Linear Programs

Abstract: Many structured large scale linear programming problems can be transformed into an equivalent problem of maximizing a piecewise linear, concave function subject to linear constraints. The concave problem can be solved in a finite number of steps using a steepest ascent algorithm. This principle is applied to block diagonal systems yielding refinements of existing algorithms. An application to the multistage problem yields an entirely new algorithm.

A Multi-Commodity Concave Cost Minimization Problem for Communication Networks

Abstract: : In this network synthesis problem a matrix giving flow requirements between each pair of points is specified, and the cost of flow in each arc is a concave function of the amount of flow. A flow pattern which fulfills the requirements at minimum cost is sought. The problem is formulated as a concave programming problem with linear constraints. All the practical difficulties of formulation and theoretical difficulties of identifying the globally minimal solution while avoiding locally minimal solutions are discussed.

Bounds for stochastic convex programs

Abstract: A maximization of a concave function subject to convex inequalities is considered when the right-hand side of the inequalities is a random vector. Bounds are established for the distribution function of the optimum under these general assumptions for the normally and uniformly distributed right-hand sides. Four kinds of bounds are shown to be the best in the sense that in extreme cases they are equal to the actual probability function itself. The approach is demonstrated on a simple example and the influence of the problem-dimensionality is discussed.