I have the problem to solve for 3 parameters of 3 nonlinear equations which result from analytic entropy maximization with constraints.  I only know of the IML/polyroot procedure to find roots and only so for polynomials. So in searching the internet I found a discussion where it was recommended to convert this problem into a minimization problem by forming minimizing the sum of the squares of these functions using proc optmodel with the option "solve with nlp".  When I do this, the solver stops after 5000 steps with "Solution Status: Iteration Limit Reached" but the objective function being 3.6E-21, "Optimality Error: 0.00768" and "Infeasibilty: 0", so pretty close to a solution.  Now, by chance, I tried also to optimize a constant function with my three equations as constraints.  This time the routine converged in only 10 iterations, with the parameter estimates being equal to the ones obtained with the first method.  While this seems to be a very convenient way to find the roots of a set of equations, I am a little bit uneasy about its theoretical foundation.  Is this method recommendable or are there easier and more sound solutions?   Thank you, Florian  ... View more