Geodesic
Method for sequential activation of limitations in~linear programming
Prikladnaâ diskretnaâ matematika, no. 3 (2018), pp. 110-125

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In this paper, we present an algorithm for solving a problem in linear programming by means of procedure of sequential activation of limitations (inclusions in calculation are made one after another) with retention of the optimality status in the generated sequence of nested polyhedrons. Due to compression of the admissible solutions area, the objective function decreases on each step at the “max” criterion of an optimality (the movement to a maximum “from above”) contrary to its growth in other methods (“from below”). Geometrically, the motion to the maximum starts from the trivially determined starting point and continues along the broken line outside of the polytope of admissible solutions. In the theoretical justification of the algorithm, the signs for the incompatibility of the system of conditions in the problem, for the uniqueness and nonuniqueness of the solution, and for its unboundedness are formulated and proved. Computer experiments demonstrate the advantages of the program implementation of this algorithm in speed and completeness of the output information over the simplex-method option of the MATLAB's library linprog program.
Keywords: linear programming, activation of limitation, MATLAB, computer experiment. 
@article{PDM_2018_3_a10,
     author = {V. S. Kolosov},
     title = {Method for sequential activation of limitations in~linear programming},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {110--125},
     publisher = {mathdoc},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2018_3_a10/}
}
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V. S. Kolosov. Method for sequential activation of limitations in~linear programming. Prikladnaâ diskretnaâ matematika, no. 3 (2018), pp. 110-125. http://geodesic.mathdoc.fr/item/PDM_2018_3_a10/