On strictly minimal elements w.r.t. preorder relations in set-valued optimization

The principal aim of this paper is to develop two algorithms for computing all strictly minimal elements of a nonempty finite family of sets in a real linear space, with respect to a preorder relation defined on the power set of that space. By implementing these algorithms in MATLAB we compute all strictly minimal elements of some test families of rectangles, with respect to -type and u-type preorder relations induced by the standard ordering cone in the Euclidean plane.