Variational analysis of marginal functions with applications to bilevel programming (Q415393)

Consider a (possibly nonsmooth) function \(F:X\times Y\to \mathbb{R}\) defined on the product of two Banach spaces. By using techniques of nonsmooth differential calculus, the authors derive optimality conditions for a bilevel program of the form \[ \text{minimize} \; F(x,y) \;\text{ subject }\; \text{ to } \;y\in S(x), \] where \[ S(x)= \text{Argmin}_{y\in G(x)}\varphi(x,y) \] is in turn the solution set to another minimization problem depending on \(x\).