A Class of Dantzig-Wolfe Type Decomposition Methods for Variational Inequality Problems
Mikhail Solodov | Luna, Juan Pablo | Sagastizábal, Claudia
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.