Title: Stochastic and graphical comparisons of the convergence property for multiple runs of non-linear programming algorithms
Author: Dewi Rahardja, Yan D. Zhao, Yongming Qu
Department of Mathematics and Computer Science, University of Indianapolis, Lilly Hall 304, 1400 East Hanna Avenue, Indianapolis, IN 46227, USA.
Eli Lilly and Company, Indianapolis, IN 46285, USA.
Eli Lilly and Company, Indianapolis, IN 46285, USA
Abstract: Non-Linear Programming (NLP) problems are often encountered in real world applications. For such problems numerous algorithms have been proposed and the convergence properties of single run of these algorithms have typically been assessed. In this article, we focus on computationally unintensive NLP algorithms with random starting values. Such algorithms enable multiple runs for a particular application and the optimum from the multiple runs is taken as the final solution. In such a scenario, the convergence property of multiple runs of an algorithm is of more interest than that of a single run. Therefore, we propose a stochastic and graphical method to assess the convergence property for multiple runs of NLP algorithms. We plot the mean best objective function values found in multiple runs versus the number of runs for several algorithms to examine how each algorithm converges and to compare among algorithms.
Keywords: algorithms comparison; nonlinear programming; NLP; multiple runs; empirical density function; mean best objective function values; convergence properties.
Int. J. of Industrial and Systems Engineering, 2007 Vol.2, No.2, pp.159 - 165
Available online: 01 Jan 2007