集值优化问题中几种有效点对的最优性条件

Several Optimality Conditions of Efficient Points for Set-valued Optimization Problems

在实赋泛空间中,引入了集值映射的二次径向切上导数的概念,将一次径向切上导数概念下成立的一些结论推广到二次径向切上导数,从而获得了5种有效点对的充分和必要条件.这种集值映射的二次径向切上导数的概念可以简化最优性条件,使得必要性和充分性条件达到统一,可以应用于集值优化问题的各种有效解中.

The concept of second-order radial epiderivatives for set-valued mappings was introduced into the real normed space, and then some results which are found true within the concept of the first-order radial epiderivatives were extended to the second-order radial epiderivatives, thus to obtain five necessary and sufficient optimality conditions for efficient points in the real normed spaces. This kind of concept of second-order radial epiderivatives for set-valued mappings can simplify optimality conditions and help achieve unity between the necessity and sufficient optimality conditions, which makes it possible for such a concept to find application in various kinds of efficient solutions for set-valued optimization problems.