Summary
International Symposium on Nonlinear Theory and its Applications
2008
Session Number:A2L-F
Session:
Number:A2L-F4
An Algorithm for Globally Minimizing a Function with Many Local Minimal Values whose Sequence is Unimodal
Hideo KANEMITSU, Hideaki KONNO, Masaaki MIYAKOSHI,
pp.-
Publication Date:2008/9/7
Online ISSN:2188-5079
Summary:
We present an algorithm for finding the global minimum of a function with many isolated local minimal function values whose (strict lower) sequence is unimodal. First, we define a univariate function such that local minimal values of the function are a unimodal sequence. Next, we introduce a new algorithm for finding the global minimum of these functions and investigate the convergence of the algorithm. We also present an algorithm for finding the global minimum of multivariate functions. We show using a numerical example that the algorithm effectively finds the global minimum with only a few function evaluations.