Dunaychuk M. Methods and algorithms of solving some continuous nonlinear problems of optimal set partition

The object is infinite-dimensional mathematical programming with Boolean variables. The aim is to create and ground some methods of solving the continuous nonlinear problems of optimal partition of some sets in an n-measurable Euclidean space into disjoint subsets; development and software implementation on their basis. The methods are methods of infinite-dimensional mathematical programming, nonsmooth optimization, operator equations solving; the methods of solving continuous linear problems of optimal set partition; functional analysis. There are mathematical statements of continuous nonlinear problems of optimal set partition with subset centers arrangement as a result of the research are formulated. Passing from the infinite-dimensional problems of optimization to dual finite-dimensional nonsmooth ones and auxiliary operator equations is substantiated. Methods and algorithms of solving the continuous nonlinear problems are developed. The originated mathematical apparatus of solving the continuous nonlinear problems of optimal set partition with subset centers arrangement is applied in case of corresponding problems with fixed subset centers. NZORM system, being a software implementation of all the suggested algorithms, is engineered. The scope is solving some practical economic, social, industrial problems, such as infinite-dimensional transportation problems, infinite-dimensional problems of factories arrangement, irrigation problems etc., that can be reduced in mathemati-cal problems statements to the continuous nonlinear problems of optimal set partition; solving some problems of theoretical optimization, statistic decisions theory and the nearest approach theory.