A greedy algorithm for minimizing a separable convex function over an integral bisubmodular polyhedron

The authors present a new greedy algoritm for minimizing a separable convex function over an integral bisubmodular polyhedron. 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 there exists at least one optimal solution in the coordinate-wise steepest descent direction from a feasible solution if it is not an optimal one.