A modification of the <Emphasis FontCategory="NonProportional">DIRECT method for Lipschitz global optimization for a symmetric function

In this paper, we consider a global optimization problem for a symmetric Lipschitz continuous function. An efficient modification of the well-known <Emphasis FontCategory="NonProportional">DIRECT (DIviding RECTangles) method called <Emphasis FontCategory="NonProportional">SymDIRECT is proposed for solving this problem. The method is illustrated and tested on several standard test functions. The application of this method to solving complex center-based clustering problems for the data having only one feature is particularly presented. Copyright Springer Science+Business Media New York 2013