An algorithm for very large sizes linear problems

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Abstract In this paper, we propose an algorithm (SC+PAM) for solving large size linear programming problem with bounded variables where we combined two methods: the selection of constraint method (SC) and the pivot adaptive method (PAM). The step of (SC+PAM), consist in first, selecting the constraints of the starting problem, and a sequence of linear sub-problems of increasing size which will be obtained by adding to the previous a set of constraints unsatisfied by the optimal solution of the current problem, the constraints to be added at each iteration being the most orthogonal to the criterion of the strarting problem. The stop criterion of (SC+PAM) is when all the constraints are satisfied and thus the solution found is opitmal for the strating problem. Thus, this method takes less computing time than (PAM), which is confirmed by numerical examples. MSC code: 90C05, 90C06, 90C51.

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