Sergienko T. Stability analysis of vector integer optimization problems

Approaches to investigating of stability of vector integer optimization problems are developed and improved. Necessary and sufficient conditions of several types of stability with respect to perturbations of initial data of vector integer optimization problems with different kinds of partial criterions and principles of optimality (Pareto, Slater or Smale) were obtained. Analysis of stability with respect to vector criterion of the integer and mixed-integer programming problems with linear partial functions were carried out. Analysis of several types of stability with respect to quadratic vector criterion of integer optimization problem were worked out on the base of results of investigating the connection of such stability with stability of some optimal and nonoptimal solutions sets. Analysis of stability with respect to constraints of multi-objective integer optimization problem are carried out for every considered type of stability. The relationship among stability of vector integer optimization problem with quadratic vector criterion and linear constraints with respect to perturbations of all initial data, stability with respect to initial data changes in linear constraints, and stability with respect to initial data changes in vector criterion is established. Approaches to regularization of vector integer optimization problem were carried out. These approaches connect with the substitution of unstable ill-posed initial problem by the perturbed stable problem.