Bilevel invex equilibrium problems with applications

In this paper, bilevel invex equilibrium problems of Hartman-Stampacchia type and Minty type [resp., in short, (HSBEP) and (MBEP)] are firstly introduced in finite Euclidean spaces. The relationships between (HSBEP) and (MBEP) are presented under some suitable conditions. By using fixed point technique, the nonemptiness and compactness of solution sets to (HSBEP) and (MBEP) are established under the invexity, respectively. As applications, we investigate the existence of solution and the behavior of solution set to the bilevel pseudomonotone variational inequalities of [Anh et al. J Glob Optim 2012, doi:10.1007/s10898-012-9870-y] and the solvability of minimization problem with variational inequality constraint.