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On the solution of convex bilevel optimization problems

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Abstract

An algorithm is presented for solving bilevel optimization problems with fully convex lower level problems. Convergence to a local optimal solution is shown under certain weak assumptions. This algorithm uses the optimal value transformation of the problem. Transformation of the bilevel optimization problem using the Fritz-John necessary optimality conditions applied to the lower level problem is shown to exhibit almost the same difficulties for solving the problem as the use of the Karush–Kuhn–Tucker conditions.

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  1. TU Bergakademie Freiberg, Freiberg, Germany

    S. Dempe & S. Franke

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  1. S. Dempe
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  2. S. Franke
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Correspondence to S. Dempe.

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The author’s work has been supported by Deutsche Forschungsgemeinschaft.

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Dempe, S., Franke, S. On the solution of convex bilevel optimization problems. Comput Optim Appl 63, 685–703 (2016). https://doi.org/10.1007/s10589-015-9795-8

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