Date of Award

Spring 1977

Document Type


Degree Name

Doctor of Engineering Science in Mechanical Engineering


Mechanical Engineering

First Advisor

Michael Pappas

Second Advisor

Harry Herman

Third Advisor

John W. Ryon

Fourth Advisor

Roman I. Andrushkiw

Fifth Advisor

Arnold Allentuch


A fast search algorithm for the solution of nonlinear mathematical programming optimization problems is presented in this thesis. A gradient search procedure is combined with a "Boundary Tracking"(BT) method using the feasible direction finding method of Zoutendijk for generating a feasible starting direction along the feasible-infeasible boundary.

The algorithm is applied to the minimum weight design of submersible, circular, cylindrical shells reinforced by equally spaced "T" type frames. This problem had produced algorithm failure in two earlier studies and was only recently solved by the Direct Search-Feasible Direction Algorithm (DSFD) which was shown by recent comparison studies to be among the fastest and most reliable mathematical programming methods available. The BT procedure was found to be substantially faster than DSFD, producing a solution with about one-eigth the effort required by DSFD.

In a general comparison study a code based on the BT algorithm was compared with twenty other codes representing most of the popular numerical optimization methods on ten test problems. These problems are such that majority of the codes tested failed to solve more than half of them. The new code proved superior to all others in overall generality and efficiency. It solved all problems and was the fastest code on the constrained problems.