Numerical Investigation of Some Potential Problems of Univariate Minimization Methods

[+] Author and Article Information
G. E. Johnson, M. A. Townsend

Department of Mechanical Engineering and Materials Science, Vanderbilt University, Nashville, TN 37235

J. Mech. Des 101(4), 663-666 (Oct 01, 1979) (4 pages) doi:10.1115/1.3454118 History: Received February 23, 1979; Online October 21, 2010


Many nonlinear programming algorithms employ a univariate subprocedure to determine the step length at each multivariate iteration. In this note, a popular polynomial approximation-interpolation univariate algorithm (DSC-P) is compared to two versions of the golden section search. One-dimensional test functions which model the behavior of barrier and penalty functions are used for the comparison. In general, the polynominal method indicates convergence in fewer function evaluations than the golden section search. However, it is significantly less reliable. Tight convergence criteria do not necessarily lead to accurate results with the polynomial-based univariate strategy. A companion paper provides a theoretical basis for the observations and gives conditions underwhich DSC-P will fail—even for strictly convex, unimodal functions and exact arithmetic.

Copyright © 1979 by ASME
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