Affine variational inequalities (AVI) are an important problem class thatgeneralize systems of linear equations, linear complementarity problems andoptimality conditions for quadratic programs. This paper describes PATHAVI, astructure-preserving pivotal approach, that can process (solve or determineinfeasible) large-scale sparse instances of the problem efficiently, withtheoretical guarantees and at high accuracy. PATHAVI implements a strategy thatis known to process models with good theoretical properties without reducingthe problem to specialized forms, since such reductions may destroy structurein the models and can lead to very long computational times. We demonstrateformally that PATHAVI implicitly follows the theoretically sound iterationpaths, and can be implemented in a large scale setting using existing sparselinear algebra and linear programming techniques without employing a reduction.We also extend the class of problems that PATHAVI can process. The paperdemonstrates the effectiveness of our approach by comparison to the PATH solverused on a complementarity reformulation of the AVI in the context ofapplications in friction contact and Nash Equilibria problems. PATHAVI is ageneral purpose solver, and freely available under the same conditions as PATH .
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