On the inverse problem of linear programming and its application to minimum weight perfect k-matching

Article Abstract:

Research was conducted to examine the inverse problem of general linear programing. The objective is to show the existence of a strongly polynomial algorithm for solving the inverse problem. The model is applied to inverse perfect k-matching problem of bipartite graph. Using l(sub 1) norm one maintained the similar structure of original problem which made it easier to solve. Results showed that there is a strongly polynomial algorithm for solving the inverse problem.

Matrices, Matrices (Mathematics), Statistical norms

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New variants of finite criss-cross pivot algorithms for linear programming

Article Abstract:

A study was conducted to generalize the first-in-last-out pivot rule and the most-often-selected-variable pivot rule for the simplex technique to the criss-cross pivot setting. The finiteness of the new criss-cross pivot variants was proven. Results indicated that the finiteness of the criss-cross algorithms A1, A2 and A3 work in a recursive manner, always solving a subproblem completely before considering a larger subproblem.

Analysis, Algorithms

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