# File numerics/src/AVI/AVI_Solvers.h¶

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Subroutines for the resolution of Affine Variational Inequalities.

Functions

int avi_caoferris(AffineVariationalInequalities *problem, double *z, double *w, SolverOptions *options)

avi_caoferris is a direct solver for AVI based on pivoting method principle for degenerate problem Choice of pivot variable is performed via lexicographic ordering Ref: “A Pivotal Method for Affine Variational Inequalities” Menglin Cao et Michael Ferris (1996)

Return
info about the convergence: 0 ok; 1 …
Parameters
• problem: structure that represents the AVI (M, q, K)
• z: on call contains the initial solution and on return holds the solution of the problem.
• w: defined as Mz + q
• options: structure used to define the solver and its parameters.

int avi_pathavi(AffineVariationalInequalities *problem, double *z, double *w, SolverOptions *options)

avi_pathavi is using PATHVI, a direct solver for VI based on pivoting method principle for degenerate problem Ref: “A structure-preserving Pivotal Method for Affine Variational Inequalities” Y.

Kim, O. Huber, M.C. Ferris, Math Prog B (2017)

Return
info about the convergence: 0 ok; 1 …
Parameters
• problem: structure that represents the AVI (M, q, K)
• z: on call contains the initial solution and on return holds the solution of the problem.
• w: defined as Mz + q
• options: structure used to define the solver and its parameters.