Titlebook: Bilevel Optimization; Advances and Next Ch Stephan Dempe,Alain Zemkoho Book 2020 Springer Nature Switzerland AG 2020 Algorithms for linear

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Fritz Schultz-Grunow,Herbert Zeibigmal control problem of partial differential equations have to be reconstructed. After verifying the existence of solutions, necessary optimality conditions are derived by exploiting the optimal value function of the underlying parametric optimal control problem in the context of a relaxation approach.

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Constraint Qualifications and Optimality Conditions in Bilevel Optimizationimality condition for the reformulation by the mathematical program with a generalized equation constraint. For the bilevel program with a nonconvex lower level program we propose a relaxed constant positive linear dependence (RCPLD) condition for the combined program.

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Algorithms for Linear Bilevel Optimizationlevel optimization problem. Most of them are exact algorithms, with only a few applying metaheuristic techniques. In this chapter, both kind of algorithms are reviewed according to the underlying idea that justifies them.

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