Nonsmooth problems in mathematical diagnostics

Different problems of practical importance, such as problems of pattern recognition, medical and technical diagnostics, identification, study of experimental data etc., can be described by mathematical models which require the solution of the problem of separation of two or more sets. In many cases the sets mentioned are inseparable, and the problem arises to ``separate'' them in the best possible way (i.e. to identify as many points as possible, to minimize the number of unidentified points). In the paper the identification problems are treated as optimization problems. More sophisticated models are described by nonsmooth optimization problems. An algorithm is suggested allowing to construct a sequence of linear criterion functions which can be used for the identification of the points of the sets.