QVILIB: A library of quasi-variational inequality test problems Quasi-variational inequalities (QVIs) are a well established and important modelling tool with several applications in different fields. Solution methods exist, but are either especially tailored to very particular classes of problems, or are investigated mainly from a theoretical point of view. However, spurred by several recent applications of QVIs in engineering, the interest in general purpose solution methods is growing. The aim of this paper is to present a collection of test problems from diverse sources which gives a uniform basis on which algorithms for the solution of QVIs can be tested and compared. All the proposed problems are implemeted in Matlab and the collection is freely available on request.