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Variational analysis of marginal functions with applications to bilevel programming. (English) Zbl 1268.90127

Consider a (possibly nonsmooth) function F:X×Y 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

minimizeF(x,y)subjecttoyS(x),

where

S(x)=Argmin yG(x) φ(x,y)

is in turn the solution set to another minimization problem depending on x.

MSC:
90C48Programming in abstract spaces
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