An Efficient One Dimensional Search Procedure

R. L. Fox, L. S. Lasdon, Arie Tamir and Margery Ratner
Additional contact information
R. L. Fox: Case Western Reserve University
L. S. Lasdon: Case Western Reserve University
Arie Tamir: Graduate School of Management, Northwestern University
Margery Ratner: Computer and Information Sciences, Case Western Reserve University

Management Science, 1975, vol. 22, issue 1, 42-50

Abstract: Many nonlinear programming algorithms utilize a one-dimensional search along directions generated by the algorithm. This paper describes a method for performing this search. The method finds 3 points which bracket the minimum, fits a quadratic through them to yield a fourth point, then fits successive cubics through 4 points, discarding one each time, until certain stop criteria are met. No gradient evaluations are required. Detailed flow charts of this procedure are given, and its performance is compared with that of 2 other algorithms. Eight test problems are used in this comparison, each solved using both exterior and interior penalty functions. The Davidon-Fleteher-Powell method is used to generate the search directions. Results show that the proposed procedure requires about 1/2 to 3/4 to the computer time of its nearest competitor, a procedure designed to be especially efficient when applied to penalty functions, and about 1/3 the time of the other competitor, the 2 point cubic search using derivatives.

Date: 1975
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