中文摘要：

引入了向量值映射的B-C-半预不变凸性概念，讨论了B-C-半预不变凸函数向量优化问题（VP）min x∈k F（z）的局部弱极小点与全局弱极小点的关系，并在弧方向可微的条件下建立了向量优化问题（VP）min x∈kF（x）与向量似变分不等式问题（VVLI）求x0∈K使得F′（x0；^τ（x，x0））￠-intC，任意x∈K的等价性。

英文摘要：

In this paper, a class of vector-valued functions, called B-C-semi-preinvex function, which are generalization of C-semi-pre- invex functions and semi-B-preinvex functions, is introduced. We study the relations between local weak minimum and global weak minimum for vector optimization problems （VP） min x∈k F（x） with B-C-semi-preinvex. Under the arcwise directionally differentiable condition, we obtain a property： if F is said to be B-C-semi-preinvex on K with respect τ, b, then the following inequality holds ^-b（y,x）（F（y）-F（x））-F′（x;^τ（y,x））∈C,arbitary x,y∈k,α∈[0,1],where lim α→0 ατ（y,x,α）=θ d/dα[ατ（y,x,α）]｜α=0^＋=^τ（y,x）,lim α→0 α^-1（y,x,α）=b（y,x）; We also discuss the vector variational-like inequality, establish an equivalence relation between the vector optimization problem （VP） minF（x） and the vector variational-like inequality （VVLI） find x0 ∈ K such as F′（x0;^τ（y,x））￠-intC.