TY - INPR A1 - Krebs, Vanessa A1 - Müller, Michael A1 - Schmidt, Martin T1 - Γ-Robust Linear Complementarity Problems with Ellipsoidal Uncertainty Sets T2 - International Transactions in Operational Research N2 - We study uncertain linear complementarity problems (LCPs), i.e., 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 [16]. There, we studied Γ-robustified LCPs for l1- and box-uncertainty sets, whereas we now focus on ellipsoidal uncertainty set. 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. KW - Robust optimization KW - Linear complementarity problems KW - Ellipsoidal uncertainty sets KW - Traffic equilibrium problems Y1 - 2019 IS - 29(1) SP - 417 EP - 441 ER - TY - JOUR A1 - Gugat, Martin A1 - Herty, Michael A1 - Müller, Siegfried ED - Piccoli, Benedetto T1 - Coupling conditions for the transition from supersonic to subsonic fluid states JF - Networks and Heterogeneous Media (NHM) N2 - We discuss coupling conditions for the p-system in case of a transition from supersonic states to subsonic states. A single junction with adjacent pipes is considered where on each pipe the gas ow is governed by a general p-system. By extending the notion of demand and supply known from traffic fiow analysis we obtain a constructive existence result of solutions compatible with the introduced conditions. KW - p-system KW - coupling conditions KW - network Y1 - 2017 U6 - https://doi.org/10.3934/nhm.2017016 VL - 12 IS - 3 SP - 371 EP - 380 ER -