Γ‐robust linear complementarity problems with ellipsoidal uncertainty sets

We study uncertain linear complementarity problems (LCPs), that is, problems in which the LCP vector q or the LCP matrix M may contain uncertain parameters. To this end, we use the concept of Γ‐robust optimization applied to the gap function formulation of the LCP. Thus, this work builds upon Krebs and Schmidt (2020). There, we studied Γ‐robustified LCPs for ℓ1‐ and box‐uncertainty sets, whereas we now focus on ellipsoidal uncertainty sets. For uncertainty in q or M, we derive conditions for the tractability of the robust counterparts. For these counterparts, we also give conditions for the existence and uniqueness of their solutions. Finally, a case study for the uncertain traffic equilibrium problem is considered, which illustrates the effects of the values of Γ on the feasibility and quality of the respective robustified solutions.