12 citations · 62 across the 15 of their papers we have counts for
15 papers
Complexity of partitioned-items response problems: matchings and perfect matchings
Christoph Buchheim, Lowig Duer, Eva Ley +2
We consider bilevel optimization problems in which leader and follower jointly construct a feasible solution for an underlying combinatorial optimization problem. Response problems…
Bilevel linear optimization belongs to NP and admits polynomial-size KKT-based reformulations
Christoph Buchheim
It is a well-known result that bilevel linear optimization is NP-hard. In many publications, reformulations as mixed-integer linear optimization problems are proposed, which sugges…
Partitioned vs. Integrated Planning of Hinterland Networks for LCL Transportation
Niklas Jost, Dorothee Henke, Ivo Hedtke +4
Utilizing existing transportation networks better and designing (parts of) networks involves routing decisions to minimize transportation costs and maximize consolidation effects.…
Parabolic optimal control problems with combinatorial switching constraints -- Part II: Outer approximation algorithm
Christoph Buchheim, Alexandra Grütering, Christian Meyer
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switc…
Parabolic optimal control problems with combinatorial switching constraints -- Part I: Convex relaxations
Christoph Buchheim, Alexandra Grütering, Christian Meyer
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switc…
An oracle-based framework for robust combinatorial optimization
Enrico Bettiol, Christoph Buchheim, Marianna De Santis +1
We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. We focus on the discrete scenario ca…
The Stochastic Bilevel Continuous Knapsack Problem with Uncertain Follower's Objective
Christoph Buchheim, Dorothee Henke, Jannik Irmai
We consider a bilevel continuous knapsack problem where the leader controls the capacity of the knapsack, while the follower chooses a feasible packing maximizing his own profit. T…
On the Complexity of Robust Bilevel Optimization With Uncertain Follower's Objective
Christoph Buchheim, Dorothee Henke, Felix Hommelsheim
We investigate the complexity of bilevel combinatorial optimization with uncertainty in the follower's objective, in a robust optimization approach. We show that the robust counter…
On the Complexity of the Bilevel Minimum Spanning Tree Problem
Christoph Buchheim, Dorothee Henke, Felix Hommelsheim
We consider the bilevel minimum spanning tree (BMST) problem where the leader and the follower choose a spanning tree together, according to different objective functions. By showi…
The robust bilevel continuous knapsack problem with uncertain coefficients in the follower's objective
Christoph Buchheim, Dorothee Henke
We consider a bilevel continuous knapsack problem where the leader controls the capacity of the knapsack and the follower chooses an optimal packing according to his own profits, w…
SDP-based branch-and-bound for non-convex quadratic integer optimization
Christoph Buchheim, Maribel Montenegro, Angelika Wiegele
Semidefinite programming (SDP) relaxations have been intensively used for solving discrete quadratic optimization problems, in particular in the binary case. For the general non-co…
An Active Set Algorithm for Robust Combinatorial Optimization Based on Separation Oracles
Christoph Buchheim, Marianna De Santis
We address combinatorial optimization problems with uncertain coefficients varying over ellipsoidal uncertainty sets. The robust counterpart of such a problem can be rewritten as a…
A coordinate ascent method for solving semidefinite relaxations of non-convex quadratic integer programs
Christoph Buchheim, Maribel Montenegro, Angelika Wiegele
We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are char…
A Feasible Active Set Method with Reoptimization for Convex Quadratic Mixed-Integer Programming
Christoph Buchheim, Marianna De Santis, Stefano Lucidi +2
We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch…
A Frank-Wolfe Based Branch-and-Bound Algorithm for Mean-Risk Optimization
Christoph Buchheim, Marianna De Santis, Francesco Rinaldi +1
We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covarian…