CONJUGATE DUALITY THEORY IN MULTIOBJECTIVE OPTIMIZATION
多目标最优化中的共轭对偶理论

This paper presents some new concepts about the conjugate map,the cone-conve-xity and the sub-differential of a vector-valued function or a general set-valued map,ect.,and discusses their relationships.The conjugate dual problem is defined in termsof the conjugate map of the perturbed objective function and a theoretical frame onconjugate duality in multiobjective optimiztion is established.The main results in thispaper are as follows:Every solution of the stable primal problem is associated with acertain solution of the dual problem,which is characterized as a subgradient of the pe-rturbed efficient vector-valued map;this pair of solutions also provides a saddle pointof the Lagrangian map.