# Class AVI¶

class AVI : public LinearOSNS

Formalization and Resolution of an Affine Variational Inequality (AVI)

This class is devoted to the formalization and the resolution of Affine variational Inequalities (AVI): given a polytopic set $$P$$, $$M\in R^{p\times p}$$ and $$q\in R^p$$,

$\text{find }z \in P\text{ such that}\quad \langle Mz+q, x - z\rangle \geq 0 \qquad \forall x \in P$

Todo:

: add “recover” function to start from old values of z and w.

For details regarding the available options, see Nonsmooth problems formulations and available solvers in users’ guide.

Public Functions

AVI(int numericsSolverId = SICONOS_AVI_CAOFERRIS)

constructor from numerics solver id

Parameters

numericsSolverId – id of numerics solver, default = SICONOS_AVI_CAOFERRIS

AVI(SP::SolverOptions options)

constructor from a pre-defined solver options set

Parameters

options – the options set

virtual ~AVI()

destructor

virtual void initialize(SP::Simulation sim)

initialize the problem (topology and so on)

Parameters

sim – the simulation that owns this OSNSPB

virtual int compute(double time)

Compute the unknown z and update the Interaction (y and lambda)

Parameters

time – current time

Returns