co-radiant集的等价表示及其在向量优化问题中的应用

The equivalent representation of co-radiant sets and its application in multi-objective optimization problems

作为特殊的抽象凸(凹)集,radiant集和co-radiant集在抽象凸分析和多目标优化问题理论中发挥着重要作用。首先建立radiant集co-radiant集的等价刻画,从而推导出它们的重要性质。然后,将重要性质应用到向量优化问题近似解的刻画中,得到关于近似解集的等价刻画。

As a special abstract convex(concave) sets,radiant sets and co-radiant sets play the important roles in abstract convex analysis and the theory of multiobjective optimization problems.We first establish the equivalent characterizations for the radiant sets and co-radiant sets.Finally,we apply important properties to the characterization of the approximate solutions of the vector optimization problems,and obtain the equivalent characterization of the approximate solution sets.