I am wondering if there is a simple example application of the Karush-Kuhn-Tucker conditions to show that a minimum exists for a multivariate minimization/optimization problem. Could anyone suggest a good reference textbook or monograph with an example?
Moreover, I am wondering if there is a computer algebra system (CAS) program or function that can be used to experiment with multivariate equations. The input to the program would be a multivariate equation, whereas the output would be some sort of analytic check for convergence (i.e. that a minimum exists). Perhaps such a program would quickly help to check equations for convergence.