Γ-robust linear complementarity problems with ellipsoidal uncertainty sets - Vanessa Krebs; Michael Müller; Martin Schmidt (International Transactions in Operational Research, 2021)
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.
Keywords: 650; robust optimization; linear complementarity problems; ellipsoidal uncertainty sets; traffic equilibrium problems