Conditions of Pareto Optimization Problems Solvability: Stable and Unstable Solvability

Abstract

The paper considers a vector (multiobjective) optimization problem with linear partial criteria and unbounded convex feasible set. Solving this problem means finding a Pareto set. The properties of two cones, the recession cone of feasible set and the cone, which partially orders this set with respect to the objective functions, are used to formulate the sufficient conditions of existence of Pareto-optimal solutions. In the case, when the perturbations of input data are possible, the sufficient conditions for stable (unstable) preservation of solvability (unsolvability) are obtained.