10 papers
Duality theory for optimistic bilevel optimization
Houria En-Naciri, Lahoussine Lafhim, Alain Zemkoho
In this paper, we exploit the so-called value function reformulation of the bilevel optimization problem to develop duality results for the problem. Our approach builds on Fenchel-…
Levenberg-Marquardt method and partial exact penalty parameter selection in bilevel optimization
Andrey Tin, Alain B. Zemkoho
We consider the optimistic bilevel optimization problem, known to have a wide range of applications in engineering, that we transform into a single-level optimization problem by me…
Newton-type method for bilevel programs with linear lower level problem and application to toll optimization
Floriane Mefo Kue, Thorsten Raasch, Alain B. Zemkoho
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 subs…
Theoretical and numerical comparison of the Karush-Kuhn-Tucker and value function reformulations in bilevel optimization
Alain Zemkoho, Shenglong Zhou
The Karush-Kuhn-Tucker and value function (lower-level value function, to be precise) reformulations are the most common single-level transformations of the bilevel optimization pr…
Semismooth Newton-type method for bilevel optimization: Global convergence and extensive numerical experiments
Andreas Fischer, Alain B. Zemkoho, Shenglong Zhou
We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the p…
Sufficient optimality conditions in bilevel programming
Patrick Mehlitz, Alain B. Zemkoho
This paper is concerned with the derivation of first- and second-order sufficient optimality conditions for optimistic bilevel optimization problems involving smooth functions. Fir…