A generalized Ekeland vector variational principle and its applications in optimization

作者：Qiu Jing Hui^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 71(10): 4705-4717.

DOI：10.1016/j.na.2009.03.034

• Ekeland vector variational principle
• Locally convex space
• Ordering cone
• Sharp efficient solution

In this paper, we give a generalized Ekeland vector variational principle. By using the principle, we extend and improve the related results in sharp efficiency. In the framework of locally convex spaces, we introduce two kinds of generalized sharp efficiencies and prove that they are equivalent. In particular, we show that a sharp efficient solution with respect to an interior point of the ordering cone is also one with respect to every interior point. Moreover, we introduce the generalized Takahashi's condition and the generalized Hamel's condition for vector-valued functions. From the generalized Ekeland principle we deduce that the two conditions are equivalent. From this, we discuss the relationship between the 'distance' of f(x) from E(f(X)) and the distance of x from E(f), where E(f(X)) denotes the efficient point set of f(X) and E(f) denotes the efficient solution set.

• 出版日期2009-11-15
• 单位苏州大学; 宿州学院