ABSTRACT
This chapter presents general, accurate and efficient numerical methods to solve the constrained problems. While this material is not part of a classical course it is extremely important since the lack of such methods has held back this important area. The analogy might be to consider where the subject of differential equations would be if there were not efficient and accurate numerical methods to solve the equations. A brief history and background of our numerical methods begins by noting the classical work on difference methods for ordinary differential equations by Henrici. This reference motivated a series of research papers by Gregory and Zeman on finite element/spline-type difference method problems which culminated in an elegant treatment involving spline matrices. The chapter considers numerical solutions using the Kuhn-Tucker methods and obtains a specific algorithm with pointwise, global error of with enough detail so that the interested reader can extend these results as desired.
