Consider a class of variational inequality problems of finding $${x^*\in S}$$ , such that $$f(x^*)^\top (z-x^*)\geq 0,\quad \forall z\in S,$$ where the underlying mapping f is hard to evaluate (sometimes its explicit form is unknown), and S has the following structure $$S=\{x\in R^n\; | \; Ax\le...