Anton Svensson – Optimization Online

Irreparable Linear Bilevel Problems with Rotations

Published: 2026/10/30

Bilevel Optimization bilevel optimization, Counterfactual explanations, existence of solutions, left-hand side parameterization, Set-valued continuity, Stability under perturbations

Classic linear bilevel optimization assumes that the upper-level decision impacts only the right-hand side of the lower-level constraints, which guarantees a solution under mild conditions. We study existence of solutions for linear bilevel problems with rotations (LBPR, for short), i.e., problems for which the upper-level decision modifies the left-hand side coefficients of the linear follower … Read more

Calmness of the Solution-Set Mapping for Linear Bilevel and Pricing Problems

Published: 2026/05/29, Updated: 2026/06/12

Bilevel Optimization Approximate feasibility, bilevel optimization, calmness, linear bilevel optimization, Outer semicontinuity, Pricing problems

We study linear bilevel and pricing problems in which the upper- and lower-level constraints’ right-hand sides are perturbed. In this setting, it is an important question, also for the validity of numerical solution schemes, if the solution-set mapping of the parametric bilevel problem is calm at the zero-perturbation. We provide the complete picture both for … Read more