Brunel University, School of Information Systems, Computing and Mathematics
Abstract
This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.In this thesis some problems in mathematical programming have been
studied. Chapter 1 contains a brief review of the problems studied
and the motivation for choosing these problems for further investigation.
The development of two algorithms for finding all the vertices of a
convex polyhedron and their applications are reported in Chapter 2.
The linear complementary problem is studied in Chapter 3 and an
algorithm to solve this problem is outlined.
Chapter 4 contains a description of the plant location problem
(uncapacited). This problem has been studied in some depth and an
algorithm to solve this problem is presented.
By using the Chinese representation of integers a new algorithm
has been developed for transforming a nonsingular integer matrix
into its Smith Normal Form; this work is discussed in Chapter 5.
A hybrid algorithm involving the gradient method and the simplex
method has also been developed to solve the linear programming problem.
Chapter 6 contains a description of this method.
The computer programs written in FORTRAN IV for these algorithms
are set out in Appendices Rl to R5. A report on study of the group
theory and its application in mathematical programming is presented
as supplementary material.
The algorithms in Chapter 2 are new. Part one of Chapter 3 is a
collection of published material on the solution of the linear
complementary problem; however the algorithm in Part two of this
Chapter is original.
The formulation of the plant location problem (uncapacited) together
with some simplifications are claimed to be original. The use of
Chinese representation of integers to transform an integer matrix into
its Smith Normal Form is a new technique.
The algorithm in Chapter 6 illustrates a new approach to solve the
linear programming problem by a mixture of gradient and simplex method
