Statistical control for nonlinear optimization

Abstract

This dissertation delineates an algorithm which provides a statistical point estimator and a confidence interval for the global optimum in a nonlinear mathematical programming problem. Further, the algorithm will also supply a value of the input vector such that the objective function when evaluated at this vector will be "close" to the global optimum. The degree of closeness depends, of course, on the effort that is expended in accumulating information on the nonlinear programming problem. An alternative procedure to the primary algorithm which utilizes prior information on the problem is presented. In addition, the small sample distributional properties of a quadratic form which is used extensively in the algorithms are explored. The primary and alternative procedures are applied to nonlinear mathematical programming problems with known global optima to illustrate the techniques.