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Γ‐robust linear complementarity problems with ellipsoidal uncertainty sets
Author(s) -
Krebs Vanessa,
Müller Michael,
Schmidt Martin
Publication year - 2022
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12988
Subject(s) - ellipsoid , complementarity theory , complementarity (molecular biology) , uniqueness , mathematical optimization , mathematics , robust optimization , linear complementarity problem , computer science , mathematical analysis , nonlinear system , physics , quantum mechanics , astronomy , biology , genetics
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 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 Γ on the feasibility and quality of the respective robustified solutions.