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On the numerical solution of a class of Stackelberg problems. (English) Zbl 0714.90077

Results of nonsmooth analysis are applied in order to enlarge the number of available numerical methods for a Stackelberg problem: minimize \(f_ L(x,y)\) subject to \(y\in \min_{s\in \Omega (x)}f_ F(x,s)\) and \(x\in \omega\); here \(f_ L\) and \(f_ F\) denote the objectives of the Leader and Follower, respectively, \(\omega\) is the set of admissible strategies of the Leader, and \(\Omega\) (x) is the set of admissible strategies of the Follower; usually \(\Omega (x)=\{y\); \(\phi^ 1(x,y)\leq 0,...,\phi^{\ell}(x,y)\leq 0\}\). The proposed numerical approaches have been tested on some simple academic examples and on a larger optimum design problem taken from J. Haslinger and P. Neittaanmäki [“Finite element approximation of optimal shape design. Theory and applications” (1988; Zbl 0713.73062)]. Comments are made about applied codes and net results including initial guess, number of function evaluations and iterations, and final accuracy.
Reviewer: C.Ursescu

MSC:

90C25 Convex programming
65K05 Numerical mathematical programming methods
49J52 Nonsmooth analysis
93A13 Hierarchical systems
49J40 Variational inequalities
91A65 Hierarchical games (including Stackelberg games)
90-08 Computational methods for problems pertaining to operations research and mathematical programming

Citations:

Zbl 0713.73062

Software:

NLPQL
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Full Text: DOI

References:

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