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Gamma-Robust Linear Complementarity Problems with Ellipsoidal Uncertainty Sets

Vanessa Krebs (vanessa.krebs***at***fau.de)
Michael Müller (mueller.mwkg***at***posteo.de)
Martin Schmidt (martin.schmidt***at***uni-trier.de)

Abstract: 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 Gamma-robust optimization applied to the gap function formulation of the LCP. Thus, this work builds upon [16]. There, we studied Gamma-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 Gamma on the feasibility and quality of the respective robustified solutions.

Keywords: Robust optimization, Linear complementarity problems, Ellipsoidal uncertainty sets, Traffic equilibrium problems

Category 1: Complementarity and Variational Inequalities

Category 2: Robust Optimization

Category 3: Applications -- OR and Management Sciences (Transportation )


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Entry Submitted: 10/10/2019
Entry Accepted: 10/15/2019
Entry Last Modified: 03/29/2021

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