Duality for max-separable problems

In this paper we propose a general duality theory for a class of so called ‘max-separable’ optimization problems. In such problems functions h:R ^k → R of the form h(x ₁, . . . , x _k ) =? max _j ? h _j (x _j ), occur both as objective functions and as constraint functions (h _j are assumed to be strictly increasing functions of one variable). As a result we obtain pairs of max-separable optimization problems, which possess both weak and strong duality property without a duality gap.