Error bounds for affine variational inequalities with second-order cone constraints

In this paper, error bounds for affine variational inequalities with second-order cone constraints are considered. Examples are given to show that, in general, Lipschitz error bounds may be invalid for affine second-order cone inclusion problems. We provide a sufficient condition (not stronger than Mangasarian-Fromovitz constraint qualification), under which a local Lipschitz error bound is valid for the variational inequality problem. Moreover, under a full row rank assumption, a local Hölder error bound is established for the variational inequality problem and the Hölder exponent is bounded by a function of problem dimensions.