Semenova N. Vector problems of discrete optimization: correctness and methods of solution

The thesis is devoted to the problems of development of the new mathematical models and methods used to solving of discrete and combinatorial vector optimization problems. Theoretical bases development of mathematical tools for research of well-posedness and solution methods of discrete optimization problems with conditions of multiobjective, possible perturbations, controllability and uncertainty of initial data are offered. The purpose of thesis is development and ground of new mathematical models, exact and approximate methods of solution of different vector problems classes of discrete optimization with the conditions of definiteness and discrete optimization problems with the conditions of uncertainty, of controllability and ambiguously set information with different principles of optimality, and also working out problems of quantitative nature: research of well-posedness and stability of vector discrete optimization problems with conditions of possible perturbations of initial data. The thesis establishes the necessary and sufficient conditions of existence for various kinds of efficient solutions of vector optimization problems with an unbounded convex closed feasible set. The research is based on applying of properties of recessive cones of feasible set and cones of perspective directions of optimization problems. Stability with respect to vector criterion and with respect to constraints for different classes of vector problems of discrete optimization is investigated. Conditions of optimality for different types of solutions are proved. The topological properties of sets of initial data for discrete optimization problem with a vector criterion are investigated.