Optimization: Application of the epsilon method

The use of Balakrishnan's epsilon method is demonstrated. Whereas most optimization schemes are based upon exact satisfaction of the system dynamics and penalty for terminal error, the epsilon method is based upon exact satisfaction of the terminal conditions and penalty for erroneous dynamics. Thus theoretical aspects of the epsilon method are discussed, a method of solution using the Rayleigh-Ritz representation and a modified Newton-Raphson minimization is described, and an optimization problem is solved. Finally, advantages and disadvantages of the epsilon method are discussed.