Complete efficiency and interdependencies between objective functions in vector optimization

Vector optimization problems in linear spaces with respect to general domination sets are investigated including corollaries to Pareto-optimality and weak efficiency. The results contain equivalences between vector optimization problems, interdependencies between objective functions and domination sets, statements about the influence of perturbed objective functions on the decision maker’s preferences and thus on the domination set, comparisons of efficiency with respect to polyhedral cones with Pareto-optimality, changes in the objective functions which restrict, extend or do not alter the set of Pareto-optima, possibilities for the use of domination sets immediately in the decision space. Conditions for complete efficiency are given.