Kadochnikova I. Methods and algorithms of solving some continuous problems of optimal set partitioning with conditions

The object is the continuous problem of optimal set partitioning, which is the objective of the infinite mathematical programming problem with Boolean variables. The aim is to develop and validate the methods for solving linear continuous problems of optimal set partitioning into subsets with centers location using additional conditions in terms of certainty and uncertainty, to construct and program release the algorithms based on them. Methods of research are functional analysis, duality theory, the theory of continuous optimal set partitioning, methods of nondifferentiable optimization. New mathematical formulation of deterministic and stochastic linear continuous problems of optimal set partitioning with centers location under additional constraints was found. The necessary conditions of optimality and solvability conditions for the above tasks were found. Methods for solving these problems were developed and validated for the first time. The knowledge of subjective characteristics of certain random parameters of the problem is sufficient to solve stochastic problems. On the basis of the developed methods new algorithms for solving deterministic and stochastic linear continuous problems of optimal set partitioning with location centers under additional conditions were created. A software product for an examined class of continuous linear problems of optimal set partitioning in terms of certainty and uncertainty was developed. Model location-allocation problems under conditions were solved.