The New Jersey Institute of Technology's
Electronic Theses & Dissertations Project

Title:	A fast boundary tracking alogorithm for constrained nonlinear mathematical programming problems
Author:	Moradi, Jacob Yaghoub
View Online:	njit-etd1977-015 (xiii, 71 pages ~ 2.7 MB pdf)
Department:	Department of Mechanical Engineering
Degree:	Doctor of Engineering Science
Program:	Mechanical Engineering
Document Type:	Dissertation
Advisory Committee:	Pappas, Michael (Committee chair) Herman, Harry (Committee member) Ryon, John W. (Committee member) Andrushkiw, Roman I. (Committee member) Allentuch, Arnold (Committee member)
Date:	1977-06
Keywords:	Nonlinear programming. Structural design.
Availability:	Unrestricted
Abstract:	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.