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Γ-Robust Linear Complementarity Problems with Ellipsoidal Uncertainty Sets

  • 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.

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Author:Vanessa Krebs, Michael Müller, Martin Schmidt
Parent Title (German):International Transactions in Operational Research
Document Type:Preprint
Language:English
Date of Publication (online):2019/10/10
Date of first Publication:2019/10/10
Release Date:2019/10/10
Tag:Ellipsoidal uncertainty sets; Linear complementarity problems; Robust optimization; Traffic equilibrium problems
Issue:29(1)
Page Number:25
First Page:417
Last Page:441
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Universität Trier
Subprojects:A05
B08
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International