The first objective of this study is to provide an up-to-date exposition of the techniques available for optimizing complex systems, and to do so in a way that unifies the theory of nondifferentiable and two-level mathematical programming. The second objective is to highlight the most effective algorithms developed for solving a particular instance of the two-level problem known as a static Stackelberg game. In approaching these objectives, close attention is paid to two ideas: (i) the integration of material on differentiable and nondifferentiable mathematical programming, and (ii) the treatment of various two-level mathematical programming problems in a unified manner. This book is intended for the use of researchers, graduate students and practitioners specializing in systems optimization and its applications. In particular, operations researchers, system designers, management scientists, control engineers and mathematicians who work on either applied or theoretical aspects of optimization will find the book useful and beneficial.