高阶广义弱Studniarski上导数及对复合集值优化问题的应用

Higher-Order Generalized Weak Studniarski Epiderivatives and Applications to Composite Set-Valued Optimization Problems

本文引入了集值映射不带低阶逼近方向的高阶广义弱Studniarski上导数,并且讨论了该导数的一些性质和运算法则.利用高阶广义弱Studniarski上导数及其性质,建立了复合集值优化问题弱有效解的高阶最优性充分条件和必要条件,并且给出了一些例子来验证所获得的结果.

In this paper,we introduce the notion of higher-order generalized weak Studniarski epiderivatives for a set-valued map without lower-order approximating di-rections and obtain chain and sum operation rules of the epiderivative.Then by apply-ing the higher-order epiderivative,we establish the optimality conditions of the weakly efficient solution for unconstrained composite set-valued optimization problems.Some illustrative examples are provided as well.