Ameso optimization: a relaxation of discrete midpoint convexity (Q2659175)

This paper presents a new class of discrete optimization problems, the Ameso optimization problems. One can see that an Ameso(C) optimization is a relaxed convex model since convex cases correspond to an Ameso(0) optimization problem. The author discusses its properties, the relationship between convexity, midpoint convexity, and Ameso optimization problem. A procedure is designed to solve Ameso(C) optimization problems and two examples are presented to illustrate the performance of the proposed procedure. Finally, the relaxation that Ameso(1) provides to the midpoint convexity is discussed.