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A popular approach for addressing uncertainty in variational inequality problems requires solving the expected residual minimization problem [X. Chen and M. Fukushima, Math. Oper. Res., 30 (2005), pp. 1022--1038, X. Chen, R. J.-B. Wets, and Y. Zhang, SIAM J. Optim., 22 (2012), pp. 649--673]. This avenue necessitates distributional information associated with the uncertainty and requires minimizing a suitably defined nonconvex expectation-valued function. Alternatively, we consider a distinctly different approach in the context of uncertain linear complementarity problems (LCPs) with a view toward obtaining robust solutions. Specifically, we define a robust solution to a complementarity problem as one that minimizes the worst case of the gap function. In what we believe is among the first efforts to comprehensively address such problems in a distribution-free environment, under prescribed assumptions on the uncertainty sets, the robust solutions to the uncertain monotone LCP can be tractably obtained throu...

On Robust Solutions to Uncertain Linear Complementarity Problems and their Variants