Greedy sets and related problems

A set D is called greedy if the greedy algorithm solves the problem max {cx |x∈D} for any c such that c1⩾…⩾cn⩾0. In previous articles we described the class of all greedy convex polyhedra in Rⁿ using the partial order technique. Here we generalize the problem and extend the class of greedy feasible sets using the so-called generalized canonical order. These results are spread onto some related problems (characterization of greedy matrices and functions).