Optimality Conditions and Solution of a Class of Multicriteria Continuous Set Partitioning Problems

Multicriterion continuous problems of partitioning sets into subsets with fixed centers under constraints are considered. Two approaches to obtaining Slater optimality conditions are proposed. An algorithm for solution of these problems is developed on their basis. Steps of meshes approximating the partitioned set are estimated and a set of parameter convolution criteria is constructed. Numerical results are given for solution of test examples.