On applicability of the algorithm of coordinate-wise lift for problems of integer programming (Q2713931)

Let a finite partially ordered set \(Q\) be given in \(\mathbb R^n\) and let \(\widetilde Q\) be the set of maximal points of \(Q\). A problem is considered of maximizing a concave separable function \(f:\widetilde Q\to\mathbb R\). Some necessary and sufficient conditions are given under which this problem can be solved by a greedy algorithm. The author also establishes another sufficient condition for applicability of the algorithm and describes a class of problems of integer programming which satisfy the condition.