Stroyeva V. Methods and algorithms of solving some continuous nonlinear multigrocery problems of optimal set partition

Object - continuous nonlinear multigrocery problems of optimum splitting of sets (OSS) which are problems of infinite-dimensional mathematical programming with Boolean values of variables. The purpose - development and justification of methods of the solution of continuous nonlinear multigrocery problems of optimum splitting of sets on subsets at restrictions, and also construction and program realization of algorithms on the basis of the developed methods. Research methods - the functional analysis, the duality theory, the theory of continuous problems of OSS, the theory of functions of sets, methods of not differentiated optimization. In work new mathematical statements of continuous nonlinear multigrocery problems of OSS on subsets both with the fixed centers of subsets, and with their placement are formulated. In terms of the theory of functions of sets necessary conditions of an optimality of objectives are received. For the first time it is developed and theoretically proved methods and algorithms of the solution of the called problems of OSS. On the basis of the constructed algorithms the software product is developed for the solution of the considered class of tasks. The software product is applied to the solution of continuous models of a number of applied infinite-dimensional problems of placement of the enterprises with simultaneous splitting of the region which has been continuously filled with consumers, into areas of consumers.