在集优化意义下的集值映射的非线性标量化

摘要

In this paper,a set optimization problem with set-valued maps is studied.A nonlinear scalarization function is introduced.Some properties of the function is discussed.By virtue of the nonlinear scalarization function,some optimization conditions for the set optimization problem are obtained.The scalar representations of set optimization problems is obtained without any convexity assumption.As an application,an existence theorem is also obtained.%本文研究了一个在集合序下的集值映射优化问题.为得到在这种集合序下的集优化问题的一些最优性条件,我们引入了一个非线性标量化函数,并研究了该函数的一些性质.通过这个非线性标量化函数,在没有任何凸性假设前提下,我们获得了这种集优化问题的标量化表示.作为应用我们还得到了一个存在性定理.