The requirement for methods of optimization arises from the mathematical complexity necessary to describe the theory of systems, processes, equipment, and devices which occur in practice. Even quite simple systems must sometimes be represented by theory which may contain approximations, by parameters which change with time, or by parameters that vary in a random manner. For many reasons the theory is imperfect, yet it must be used to predict the optimum operating conditions of a system such that some performance criterion is satisfied. At best such theory can predict only that the system is near to the desired optimum. Optimization methods are then used to explore the local region of operation and predict the way that the system parameters should be adjusted to bring the system to optimum.