Trajectory-based methods for solving nonlinear and mixed integer nonlinear programming problems

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2015.I would like to acknowledge a number of people who contributed towards the completion of this thesis. Firstly, I thank my supervisor Professor Montaz Ali for his patience, enthusiasm, guidance and teachings. The skills I have acquired during this process have infiltrated every aspect of my life. I remain forever grateful. Secondly, I would like to say a special thank you to Professor Jan Snyman for his assistance, which contributed immensely towards this thesis. I would also like to thank Professor Dominque Orban for his willingness to assist me for countless hours with the installation of CUTEr, as well as Professor Jose Mario Martinez for his email correspondence. A heartfelt thanks goes out to my family and friends at large, for their prayers, support and faith in me when I had little faith in myself. Thank you also to my colleagues who kept me sane and motivated, as well as all the support staff who played a pivotal roll in this process. Above all, I would like to thank God, without whom none of this would have been possible