DC Algorithms in Nonconvex Quadratic Programming and Applications in Data Clustering

1) The R-linear convergence of the Proximal DC decomposition algorithm (Algorithm B) and the asymptotic stability of that algorithm for the given IQP problem, as well as the analysis of the influence of the decomposition parameter on the rate of convergence of DCA sequences;
2) The solution existence theorem for of the minimum sum-of-squares clustering problem (MSSC problem) together with the necessary and sufficient conditions for a local solution of the problem, and three fundamental stability theorems for the MSSC problem when the data set is subject to change;
3) The analysis and development of the heuristic incremental algorithm of Ordin and Bagirov together with three modified versions of the DC incremental algorithms of Bagirov, including some theorems on the finite convergence and the Q-linear convergence, as well as numerical tests of the algorithms on several real-world databases.