Brila A. Attainability of optimum solutions of the multicriteria optimization problems of linear programming on the weighed sum of criteria of equal importance

The thesis is devoted to the problem of attainability of optimum solutions of lexicographic, lexicographic-lexicographical, pareto-lexicographical and lexicographic-pareto optimization problems on the weighed sum of criteria of equal importance. The method of finding of attainable optimum solutions of multicriteria optimization problems in transitional subordination is developed. It based on the reducing of these problems to the proper linear programming problems. The approach for solving of multicriteria optimization problems in complete transitional subordination by their reducing to the proper multicriteria problems with smaller quantity of criteria is proposed. Based on the use of symplex method the approach for improvement of value of some scalar criterion on the Pareto set, is grounded. This method allows to solve some subsets of problems of lexicografic-pareto optimization.