Convergence Rate, Chebyshev's Inequality, and Financial Policy

Abstract

This paper applies the dynamic quadratic regression for global optimization and provides a global convergence theory. It tests the probability p value of the convergence to the global optimum under the time-invariant policy rule. Its nonlinear optimization does imply the existence of a stable solution. A new test of p values supplements the F, student t and Neyman's test statistics for the stable region, which otherwise vary with time or sample sizes and are not robust to abnormality. The original model is approximated by a smooth and strictly concave differential equation. It is approximated by an improved logistic quadratic regression, which solves the second-order differential equation and refines Chebyshev's inequality. It detects the deviation of the sample mean from the fixed point. With either no iterations or a small number of iterations, this algorithm outperforms most other iterative algorithms for some class of optimization problems. The nonlinear system is indefinite in sign. It is solved as a switching model. Around this turning point, the feedback rule has parameters systematically altering in sign. Using seven theorems, it proves that x* is the primary solution of =f(x)=0 and denotes the multivariate optimum equilibrium. It illustrates the sequential quality control and the predator-prey models.