A special partitioning algorithm for solving linear programming problems with embed-ded network structure is presented. As an example of such a problem the minimum-cost network flow problem under additional linear constraints can be considered. This algorithm is a primal simplex basis partitioning method that uses special updating and labeling procedures to accelerate computations involving the network linear programming interface. These procedures are discribed in detail to develop an efficient...
The paper based on B. Martos’ ideas (B. Martos, Nonlinear programming theory and methods, Akademiai Kiado, Budapest 1975. Polish translation PWN 1983) presents theoretical results concerning quasiconvex and pseudoconvex functions.
This paper describes an efficient network simplex algorithm for solving minimum-cost network flow problems. The algorithm derives from a theoretical characterization of the network topology of the basis embodied in a specially constructed basis tree. Experimentation with large sparse mini- mum-cost network flow problems has shown that in practice good implemen-tation of the network simplex method is more efficient than other implemen-tations based on special network flow methods.
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