Consider a class of variational inequality problems of finding <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${x^*\in S}$$</EquationSource> </InlineEquation>, such that <Equation ID="Equa"> <EquationSource Format="TEX">$$f(x^*)^\top (z-x^*)\geq 0,\quad \forall z\in S,$$</EquationSource> </Equation> where the underlying mapping f is hard to evaluate (sometimes its explicit form is unknown), and S has the following structure <Equation ID="Equb"> <EquationSource Format="TEX">$$S=\{x\in R^n\; | \;...</equationsource></equation></equationsource></equation></equationsource></inlineequation>