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Necessary optimality conditions for Stackelberg problems. (English) Zbl 0802.49007
Summary: First-order necessary optimality conditions are derived for a class of two-level Stackelberg problems in which the followers’ lower-level problems are convex programs with unique solutions. To this purpose, generalized Jacobians of the marginal maps corresponding to followers’ problems are estimated. As illustrative examples, two discretized optimum design problems with elliptic variational inequalities are investigated. The theoretical results may be used also for the numerical solution of the Stackelberg problems considered by nondifferentiable optimization methods.

49J40 Variational inequalities
Full Text: DOI
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