Geometrical methods for the solution of a class of convex programming problems
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Date
2004-11-24
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Abstract
In this thesis, we suggest geometrical methods for the solution of convex programming problems with linear objective functions, with special emphasis on linear programming problems defined on Euclidean space. One method that we propose is based on a rigid rotation of Cartesian coordinates and a second method uses orthogonal projections to generate a monotonic sequence which is induced by an optimal sequence.
It is found that these methods enrich the theory of convex optimization and also simplify the process of solving the class of problems studied. For purposes of demonstrating the comparative efficiency of these methods relative to some traditional ones, sample problems in 2 and 3 dimensional Euclidean space are solved in detail and some algorithms and computer codes for implementing the methods are also provided. It is found that in many cases our method is easier to implement.
We find that for the particular case of low dimensional linear programming problems with a large number of constraints, our optimal sequence method is more efficient than the simplex algorithm.
Description
A thesis submitted to the Department of Mathematics,
Kwame Nkrumah University of Science and Technology in partial
fulfilment of the requirements for the award of Doctor of Philosophy degree in Mathematics, 2004