A greedy algorithm for minimizing a separable convex function over a finite jump system

The authors present a greedy algorithm for minimizing a separable convex function over a finite jump system , where E is a nonempty finite set and is a nonempty finite set of integral points in satisfying a certain exchange axiom. The concept of jump system was introduced by A. Bouchet and W.H. Cunningham. A jump system is a generalization of an integral bisubmodular polyhedron, an integral polymatroid, a (poly)-pseudomatroid and a delta-matroid, and has combinatorially nice properties. The algorithm starts with an arbitrary feasible solution and a current feasible solution incrementally moves toward an optimal one in a greedy way. The authors also show that the greedy algorithm terminates after changing an initial feasible solution at most times, where for each and