Introduction.- Introduction to Clustering.- Clustering Algorithms.- Nonsmooth Optimization Models in Cluster Analysis.- Nonsmooth Optimization.- Optimization based Clustering Algorithms.- Implementation and Numerical Results.- Conclusion.

Adil M. Bagirov is currently an Associate Professor at School of Science, Engineering and Information Technology, Federation University Australia, Ballarat, Australia. He received a master degree in Applied Mathematics from Baku State University, Azerbaijan in 1983, and the Candidate of Sciences degree in Mathematical Cybernetics from the Institute of Cybernetics of Azerbaijan National Academy of Sciences in 1989 and PhD degree in Optimization from Federation University Australia (formerly the University of Ballarat), Ballarat, Australia in 2002. He worked at the Space Research Institute (Baku, Azerbaijan), Baku State University (Baku, Azerbaijan), Joint Institute for Nuclear Research (Moscow, Russia). Dr. Bagirov is with Federation University Australia (Ballarat, Australia) since 1999. He currently holds the Associate Professor position at this university. He has won five Australian Research Council Discovery and Linkage grants to conduct research in nonsmooth and global optimization and their applications. He was awarded the Australian Research Council Postdoctoral Fellowship and the Australian Research Council Research Fellowship. His main research interests are in the area of nonsmooth and global optimization and their applications in data mining, regression analysis and water management. Dr. Bagirov has published a book on nonsmooth optimization, more than 150 journal papers, book chapters and papers in conference proceedings.

Napsu Karmitsa has been a Docent (Associate Professor) of Applied Mathematics at the Department of Mathematics and Statistics at the University of Turku, Finland, since 2011. She obtained her MSc degree in Organic Chemistry in 1998 and PhD degree in Scientific Computing in 2004 both from the University of Jyväskylä, Finland. At the moment, she holds a position of Academy Research Fellow at the University of Turku. Her research is focused on nonsmooth optimization and analysis. Special emphasis is given to nonconvex, global and large-scale cases. She is also studying theory of generalized pseudo and quasiconvexities for nonsmooth functions, developing numerical methods for solving nonsmooth, possible nonconvex and large-scale optimization problems and applying these method for solving data mining problems.

Sona Taheri is currently a Research Fellow at the School of Science, Engineering & Information Technology, Federation University Australia. Dr. Taheri has been at this University since 2009. She received her PhD degree in Mathematics from Federation University Australia (formerly the University of Ballarat) in 2012. Underpinning this is her Master degree in Applied Mathematics and Bachelor of Science in Pure Mathematics through University of Tabriz Iran completed in 2004 and 2001, respectively. Her research interests lie in the areas of optimization, particularly nonsmooth nonconvex optimization, and their applications in data mining, in particular cluster analysis and regression analysis.