Date of Award

5-1-2005

Document Type

Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

First Advisor

Dr. Stephen From

Abstract

The gradient search fails in an optimization problem where the objective function is not differentiable--such as nonlinear multiregressions based on generalized Choquet integrals. In cases such as this, we may replace the gradient search with a pseudo gradient search to determine the optimal search direction. The pseudo gradient can be obtained algorithmically from a data set containing the objective attribute and relevant arguments of the objective function. The algorithm for the pseudo gradient search is based on a neural network model which uses statistical techniques such as root mean square error to determine the optimal search direction and the optimal step length. Similar to the gradient search, the pseudo gradient search has a fast convergence rate, but a disadvantage is how easily it falls in a local extrema. Hence, choosing a suitable initial point for the pseudo gradient search is rather important. A genetic algorithm is used as an initialization method because it has the advantage of being a global search, but it is only allowed to run for a limited number of iterations due to its slow convergence rate. The pseudo gradient search may be widely applied in nonlinear multiregression, classification, and decision making.

Comments

A Thesis Presented to the Department of Mathematics and the Faculty of the Graduate College University of Nebraska In Partial Fulfillment of the Requirements for the Degree Master of Arts University of Nebraska at Omaha Copyright 2005 Marie Louise Spilde

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