Conjugate duality for vector-maximization problems (Q624559)

The authors use the concept of conjugacy and contend that the conjugate of a polyhedral concave nondecreasing homogeneous function is also a polyhedral concave nondecreasing homogeneous function. In this way they extend the conjugate duality to a larger but closed class of maximization problems and obtain generalization of earlier result by the first author [Vietnam J. Math. 32, No. 2, 209--218 (2004; Zbl 1139.91356)]. The authors also apply conjugate duality for a vector-maximization problem. A conjugate dual for a given vector-optimization problem is formulated and it is claimed that the presented conjugate duality is involutary. Other results like characterizing (weak) Pareto efficient solutions are also discussed.