Trust Regions and the Quadratic Assignment Problem

The quadratic assignment problem (QAP) belongs to the class of NP -hard combinatorial optimization problems. Although it has been studied extensively over the past 35 years, problems of size n 15 still prove to be intractable. Since good lower bounds are necessary to solve larger problem instances, we discuss the class of eigenvalue bounds for QAP and extend previous results of these continuous optimization approaches for QAP. Since these approaches include trust region techniques and optimization over partial orders, new results for these areas are obtained, as well. i Acknowledgements My deepest appreciation goes to my supervisor, Henry Wolkowicz, for his guidance, patience and encouragement during my studies. No question or idea did seem to be too trivial, to not to be answered and considered by him. I was happy to be his student. I would like to acknowledge the Austrian Bundesministerium f ur Wissenschaft und Forschung, the Exportakademie der  Osterreichischen Bundeswirtschaftskammer, and the Department of Combinatorics and Optimization for their nancial support. I want to thank these institutions for making my studies at the University of Waterloo possible. I would also like to thank Franz Rendl, Technische Universitat Graz, Austria for providing parts of the test data used in this thesis. But most of all, I wish to thank my wife Helga for her love and continuous encouragement. She gives me the strength to pursue my dreams.