STATISTICAL OPTIMIZATION WITH AVERAGING APPLIED TO A 125 VARIABLE AND 125 NONLINEAR SYSTEM OF EQUATIONS

摘要

The fields of linear algebra and subsequent linear programming have made great strides in solving large scale systems of equations and linear optimization problems. However, so many times in the real worlds of big business, science and economics, the truly practical models are nonlinear. Therefore, with linear programing and linear algebra one obtains the exact solution to the wrong question. However, some of the linear models are accurate enough to be very useful. Presented here will be statistical optimization (or multi stage Monte Carlo optimization) simulation with modal averaging applied to a 125 variable system of 125 nonlinear equations and solved for the true optimal solution with no equation errors. Then a nonlinear system with no solution will be studied to see that even in that case a perhaps useful approximation solution can be produced with multi stage Monte Carlo optimization simulation.