Preprint A706/2011
A Class of Dantzig-Wolfe Type Decomposition Methods for Variational Inequality Problems

Mikhail Solodov | Luna, Juan Pablo | Sagastizábal, Claudia

**Keywords: **
Variational inequality | decomposition | Dantzig–Wolfe decomposition | Josephy–Newton approximation | Jacobi approximation | variational equilibrium.

We consider a class of decomposition methods for
variational inequalities, which is related to the classical
Dantzig--Wolfe decomposition of linear programs.
Our approach is rather general, in that it can be used with
certain types of set-valued
or nonmonotone operators, as well as with various kinds of approximations
in the subproblems of the
functions and derivatives in the single-valued case. Also,
subproblems can be solved approximately. Convergence is established
under reasonable assumptions. We also report numerical
experiments for computing variational equilibria of the
game-theoretical models of electricity markets.
Our numerical results illustrate
that the decomposition approach allows to solve
large-scale problem instances otherwise
untractable if the widely used PATH solver is applied
directly, without decomposition.