On the relation between affinely adjustable robust linear complementarity and mixed-integer linear feasibility problems

Abstract

We consider adjustable robust linear complementarity problems and extend the results of Biefel et al. (SIAM J Optim 32:152–172, 2022) towards convex and compact uncertainty sets. Moreover, for the case of polyhedral uncertainty sets, we prove that computing an adjustable robust solution of a given linear complementarity problem is equivalent to solving a properly chosen mixed-integer linear feasibility problem.

Adjustable Robust Energy Operation Planning under Uncertain Renewable Energy Production

“…AARC problems are closely related to affinely adjustable robust complementary problems, which are investigated in [27] regarding the existence and uniqueness of robust solutions. Moreover, these kinds of problems allow for a mixed-integer programming formulation that can be used to compute solutions [27,28].…”