向量优化中的变分模型与集值分析

Variational Models and Set-valued Analysis in Vector Optimization

        陈光亚(中国科学院数学与系统科学研究院 北京100080)
        汪寿阳(中国科学院数学与系统科学研究院 北京100080)

         向量优化;变分分析;集值分析

        介绍了在向量优化理论与变分分析方面的研究工作中取得的一批得到国际同行好评的研究成果。该成果 2 0 0 0年获“ISI经典引用奖” ,2 0 0 1年获中国科学院自然科学奖一等奖。

        We have proposed firstly the vector variational inequality with variable partially ordering and the vector complementarity problem in the world. These mathematical models have become a new research direction in optimization theory field. We establish the Minimax inequalities for vector valued and set valued mappings. These work answer partially an open question by Ferro, an Italy mathematician. We obtain an unified necessary and sufficient optimality condition. For set valued optimization problems, by using original contingint derivative of set valued maps, we establish the vector versions and set valued versions of Ekeland’s variational principle, Caristi Kirt fixed point theorem, Flower Petal theorem and Drop theorem and prove the equivalence among these theorems. We establish firstly the alternative theorem of set valued optimization problems. Due to these research works we win "ISI Citation Classic Award" and First Class of National Science Award of CAS.