Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/284789 
Year of Publication: 
2021
Citation: 
[Journal:] International Transactions in Operational Research [ISSN:] 1475-3995 [Volume:] 29 [Issue:] 1 [Year:] 2021 [Pages:] 417-441
Publisher: 
Wiley, Hoboken, NJ
Abstract: 
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.
Subjects: 
robust optimization
linear complementarity problems
ellipsoidal uncertainty sets
traffic equilibrium problems
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by-nc-nd Logo
Document Type: 
Article
Document Version: 
Published Version

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