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Variational analysis of marginal functions with applications to bilevel programming. (English) Zbl 1268.90127
Consider a (possibly nonsmooth) function $F:X\times Y\to \mathbb{R}$ 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 $x$.

90C48Programming in abstract spaces
Full Text: DOI
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