Some techniques of optimization

Some common analytical and numerical techniques of finding the maximum or a minimum of multivariable functions are presented. The analytical methods given are Lagrange´s method of undetermined multipliers, linear and dynamic programming; the numerical methods given are the univariate, factorial, steepest-ascend or-descend, and direct search. Wherever possible, examples are worked out to illustrate the applicability and the limitations of the method as well as the mechanics of obtaining a solution.