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arXiv · 2010.11662

Newton-type method for bilevel programs with linear lower level problem and application to toll optimization

Floriane Mefo Kue·Thorsten Raasch·Alain B. Zemkoho
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Abstract

We consider a bilevel program involving a linear lower level problem with left-hand-side perturbation. We then consider the Karush-Kuhn-Tucker reformulation of the problem and subsequently build a tractable optimization problem with linear constraints by means of a partial exact penalization. A semismooth system of equations is then generated from the later problem and a Newton-type method is developed to solve it. Finally, we illustrate the convergence and practical implementation of the algorithm on the optimal toll-setting problem in transportation networks.

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Floriane Mefo Kue, Thorsten Raasch, Alain B. Zemkoho. 2020-10-22. Newton-type method for bilevel programs with linear lower level problem and application to toll optimization. https://arxiv.org/abs/2010.11662

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