The paper deals with the problem of characterizing Pareto optima (efficient solutions) for the difference of two mappings vector-valued in a finite or infinite-dimensional preordered space. Closely related to the well-known optimality criterion of scalar DC optimization, a mixed vectorial condition is obtained in terms of both strong (Fenchel) and weak (Pareto) <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\epsilon $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">ϵ</mi> </math> </EquationSource> </InlineEquation>-subdifferentials that completely characterizes the exact or approximate weak efficiency. This condition also allows to deal with some special restricted mappings. Moreover, the condition established in the literature in terms of strong <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$\epsilon $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">ϵ</mi> </math> </EquationSource> </InlineEquation>-subdifferentials for characterizing the strongly efficient solutions (usual optima), is shown here to remain valid without assuming that the objective space is order-complete. Copyright Springer Science+Business Media New York 2015
