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Geometry Inspired Algorithms for Linear Programming

In this paper we discuss some novel algorithms for linear programming inspired by geometrical considerations and use simple mathematics related to finding intersections of lines and planes. All these algorithms have a common aim: they all try to approach closer and closer to “centroid” or some “centrally located interior point” for speeding up the process of reaching an optimal solution! Imagine the “line” parallel to vector C, where CTx denotes the objective function to be optimized, and further suppose that this “line” is also passing through the “point” representing optimal solution. The new algorithms that we propose in this paper essentially try to reach at some feasible interior point which is in the close vicinity of this “line”, in successive steps. When one will be able to arrive finally at a point belonging to small neighborhood of some point on this “line” then by moving from this point parallel to vector C one can reach to the point belonging to the sufficiently small neighborhood of the “point” representing optimal solution.