ON A CLASS OF GLOBAL OPTIMIZATION TEST ... - CiteSeerX
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ON A CLASS OF GLOBAL OPTIMIZATION TEST ... - CiteSeerX
Among the global optimization test problems, there is a class of functions, which ... Suppose we have F = F(x, y, z) and all the three partial derivatives have the.
ON A CLASS OF GLOBAL OPTIMIZATION TEST FUNCTIONS Crina Grosan∗, Ajith Abraham†
Abstract: This paper provides a theoretical proof illustrating that for a certain class of functions having the property that the partial derivatives have the same equation with respect to all variables, the optimum value (minimum or maximum) takes place at a point where all the variables have the same value. This information will help the researchers working with high dimensional functions to minimize the computational burden due to the fact that the search has to be performed only with respect to one variable. Key words: Multidimensional functions, global optimization, first partial derivatives Received: November 5, 2008 Revised and accepted: March 15, 2009
1.
Introduction
Among the global optimization test problems, there is a class of functions, which has not been treated until now separately by any of the conventional deterministic and stochastic approaches. In this context, we refer to the functions for which the first partial derivatives with respect to all variables have the same equation. For example, let us consider the Rastrigin function given by: F : [−5.12, 5.12]n →
