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 Gamma-robust optimization applied to the gap function formulation of the LCP. Thus, this work builds upon Krebs and Schmidt (2020). There, we studied Gamma-robustified LCPs for l(1)- 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 Gamma on the feasibility and quality of the respective robustified solutions.

Automated summary

The study focuses on uncertain linear complementarity problems (LCPs) with uncertain parameters in the LCP vector q or the LCP matrix M. By applying Gamma-robust optimization to the gap function formulation of the LCP, conditions for tractability of robust counterparts are derived. Existence and uniqueness conditions for these counterparts' solutions are also provided. A case study on an uncertain traffic equilibrium problem illustrates the impact of Gamma values on the feasibility and quality of the robustified solutions.