向量优化问题(C,ε)弱有效的一个非线性标量化性质（英文）

A Nonlinear Scalarization Characterization of Weakly (C,ε)-Efficient Solutions in Vector Optimization

非线性标量化研究正在成为向量优化领域中的研究热点之一。有文献在co-radiant集的基础上提出了一种新的(C,ε)-弱有效解并利用Gerstewitz泛函给出了这种新的一个必要条件,它统一了几种经典的近似解。利用Hiriart-Urruty等人提出的非线性标量化函数,建立了(C,ε)-弱有效解的一个必要条件。

In recent years, the research of nonlinear scalarization method has become a research focus. Recently, Gutierrez et al. proposed a new type of efficiency based on co-radiant set which called （C,ε）-efficient solution in vector optimization and gave a necessary condition by the Gerstewitz function. This new notion of efficiency unifies some well-known concepts introduced previously in the literature. In this paper, we establish a new necessary condition via the A function for weakly （C,ε）-efficient solution. This can be used to obtain the （C,ε）-efficient solution set by solving the scalar optimization.