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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Bilevel Optimal Control: Existence Results and Stationarity Conditionse of them has to solve an optimal control problem of ordinary or partial differential equations. Such models are referred to as bilevel optimal control problems. Here, we first review some different features of bilevel optimal control including important applications, existence results, solution app

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https://doi.org/10.1007/978-3-030-05216-4 hierarchical interactions. Nevertheless it is only recently that theoretical and numerical developments for Multi-Leader-Follower problems have been made. This chapter aims to propose a state of the art of this field of research at the frontier between optimization and economics.

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https://doi.org/10.1007/978-94-007-4954-2imality 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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Alvar D. Gossert,Wolfgang Jahnkelevel 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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Fritz Schultz-Grunow,Herbert Zeibigly, we give reference to numerical approaches which have been followed in the literature to solve these kind of problems. We concentrate in this chapter on nonlinear problems, while the results and statements naturally also hold for the linear case.

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1931-6828 emerging applications, particularly in data analytics, secur.2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg’s habilitation thesis “Marktform und Gleichgewicht,” which formed the roots of bilevel optimization. Research on the topic has grown tremendously since its introduction

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