A class of Dantzig-Wolfe type decomposition methods for variational inequality problems

作者：Luna Juan Pablo; Sagastizabal Claudia; Solodov Mikhail^*

来源：Mathematical Programming, 2014, 143(1-2): 177-209.

DOI：10.1007/s10107-012-0599-7

• 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 may be solved approximately. Convergence is established under reasonable assumptions. We also report numerical experiments for computing variational equilibria of the game-theoretic models of electricity markets. Our numerical results illustrate that the decomposition approach allows to solve large-scale problem instances otherwise intractable if the widely used PATH solver is applied directly, without decomposition.

• 出版日期2014-2