The fields of computer science and optimization greatly influence each other, and this book is about one important connection between the two: complexity theory. Complexity theory underlies computer algorithms and is used to address such questions as the efficiency of algorithms and thepossibility of algorithmic solutions for particular problems. Furthermore, as optimization problems increase in size with hardware capacity, complexity theory plays a steadily growing role in the exploration of optimization algorithms. As larger and more complicated problems are addressed, it ismore important than ever to understand the asymptotic complexity issues. This book describes some of the key developments in the complexity aspects of optimization during the last decade. It will be a valuable source of information for computer scientists and computational mathematicians.