Abstract
We consider bilevel problem in the following formulation. The follower problem is a convex quadratic problem which linearly depends on the leader variable. The leader problem is a quadratic problem. We are looking for an optimistic solution. Optimal value function of the follower problem is used to reformulate bilevel problem as a standard (one-level) optimization problem. By this way we obtain a nonconvex multiextremal problem with implicit nonconvex constraint generated by the optimal value function. We show how to construct an explicit piecewise quadratic function which is support to the optimal value function at a given point. Usage of the support functions allows us to approximate the implicit one-level problem by a number of explicit nonconvex quadratic problems. In our talk we describe an iterative procedure based on such approximation.
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Acknowledgements
This work is supported by the Russian Science Foundation (project 17-11-01021).
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Khamisov, O. (2018). Quadratic Support Functions in Quadratic Bilevel Problems. In: Kliewer, N., Ehmke, J., Borndörfer, R. (eds) Operations Research Proceedings 2017. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-89920-6_15
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DOI: https://doi.org/10.1007/978-3-319-89920-6_15
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