Γ-robust linear complementarity problems with ellipsoidal uncertainty sets

Krebs V, Müller M, Schmidt M (2021)

Publication Type: Journal article

Publication year: 2021

Journal

International Transactions in Operational Research Blackwell Publishing

DOI: 10.1111/itor.12988

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.

Authors with CRIS profile

Vanessa Krebs Economics - Discrete Optimization - Mathematics (EDOM) Michael Müller Economics - Discrete Optimization - Mathematics (EDOM)

Involved external institutions

Universität Trier DE Germany (DE)

How to cite

APA:

Krebs, V., Müller, M., & Schmidt, M. (2021). Γ-robust linear complementarity problems with ellipsoidal uncertainty sets. International Transactions in Operational Research. https://dx.doi.org/10.1111/itor.12988

MLA:

Krebs, Vanessa, Michael Müller, and Martin Schmidt. "Γ-robust linear complementarity problems with ellipsoidal uncertainty sets." International Transactions in Operational Research (2021).

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