This book provides extensions to mathematical techniques of nonlinear optimization theory, as applies these techniques to provide self-contained treatments for various versions of the benchmark model of optimal economic growth. These models and solving methods are normally based on the traditional concepts and assumptions of nonlinear optimization, including optimality conditions, local optimality, global optimality and convexity. As an effort to contribute to the further development of the methods for optimization and their applications in economics, this monograph focuses on the necessary...