Modified Simplex Splitting Algorithm for Finding Feasible Solution of Systems of Linear Inequalities
TL;DR: The existing simplex splitting algorithm for finding a feasible solution of systems of linear inequalities is modified by evolving a vertex-determination technique that is able to determine the feasible solution whenever it exists and to detect infeasibility whenever it occurs.
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Abstract: In this paper the existing simplex splitting algorithm for finding a feasible solution of systems of linear inequalities is modified by evolving a vertex-determination technique. The existing algorithm cannot determine when the system of linear inequalities is infeasible hence the need for a modification. The modified algorithm is able to determine the feasible solution whenever it exists and to detect infeasibility whenever it occurs. The modified algorithm is tested on a problem that has a feasible solution and also on a problem that has no feasible solution and is found to work perfectly well.
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Citations
•Journal Article
An orthogonal projection algorithm for solving quadratic programming problems
TL;DR: This paper combines the classical method of unconstrained optimization, the methods for solving linear programming problems and the orthogonal projection technique to evolve a new algorithm for solving quadratic programming problems.
References
The Relaxation Method for Linear Inequalities
T. S. Motzkin,I. J. Schoenberg +1 more
TL;DR: In this article, a closed set of points in the n-dimensional euclidean space En is considered, and the closest point to the set A is defined as a point p such that there is no point p 1 which is point-wise closer than p to A.
583
An old linear programming algorithm runs in polynomial time
Boris Yamnitsky,Leonid A. Levin +1 more
- 03 Nov 1982
TL;DR: A modification of Method of Centralized Splitting presented in [L65], which differs from EA in two essential respects; it is admitted, that, several (q(n))splittings of the n-dimensional simplex may be needed before the remaining polyhedron can be enclosed into a simplex of a smaller volume.
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