A Class of B-C-semi-preinvex Functions
Zhu Jian-guang · Chongqing Shifan Daxue xuebao. Ziran kexue ban · 2007
In this paper,a class of vector-valued functions,called B-C-semi-preinvex function,which are generalization of C-semi-preinvex 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) minx∈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(y,x)(F(y)-F(x))-F′(x;(y,x))∈C,x,y∈K,α∈,where limα→0ατ(y,x,α)=θddα[ατ(y,x,α)]α=0+=(y,x),limα→0α-1b(y,x,α)=(y,x);We also discuss the vector variational-like inequality,establish an equivalence relation between the vector optimization problem(VP) minx∈KF(x) and the vector variational-like inequality(VVLI) find x0∈K such as F′(x0;(y,x))-intC.