Duality and optimality conditions in abstract concave maximization

There is no doubt that one of the most important domains of optimization theory is concave maximization, the most delicate problems of which are the duality theory and the necessary and sufficient optimality conditions. Duality theory for one-objective concave maximization is, how it is generally known, already completely developed. For vector optimization, however, the duality question is mote complicated, since the dual gap in scalar optimization cannot be easily transformed into vector optimization. The literature devoted to duality in vector optimization can be divided into two groups. In the first group duality is developed on the basis of the concept of conjugate maps (see Tanino, Sawaragi [12], Zowe [13], Gros [14]) and the results present a generalization of FencheFs duality theorem.