On Continuous Optimization Methods in Data Mining — Cluster Analysis, Classification and Regression — Provided for Decision Support and Other Applications

Optimization is an area of mathematics that finds an optimum (minimum or maximum) of some function defined in a finite or infinite set. If the functions used for the problem formulation are continuous or piecewise continuous, we obtain a continuous optimization problem. When some practical task is formulated in the form of optimization problem, the success in its solution depends mainly on the quality of a mathematical model and on the choice of an appropriate method of the model solution. Data mining today can be considered as an interdisciplinary research which employs applied mathematics and computational statistics. It treats data obtained in experiments, records, measurements, questionnaires, etc., and aims at modeling, prediction and decision support. In the paper we consider continuous optimization methods in solution of some specific problems arising in data mining: clustering, classification and regression. The results discussed are recently obtained by the members of EURO Working Group on Continuous Optimization (EUROPT) and are based on the theory and methods of continuous optimization.