Summary: Computational Mathematics and Mathematical Physics. Vol. 37. No. 11, 1997, pp. 12851296.
Translated from Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki.
Vol. 37. No. 11, 1997, pp. 13271339.
Equilibrium Programming: Proximal Methods
Revised October 10, 2004
Abstract The equilibrium-programming problem is formulated. Its relation to
game settings is discussed. To solve this problem, implicit and explicit proximal-
regularization methods using conventional and modied Lagrange functions are sug-
gested. The convergence of these methods to the equilibrium solutions is proven.
1. FORMULATION OF THE PROBLEM
The equilibrium-programming problem can be formulated as follows. Find a xed
that satises the following extremal inclusion with functional constraints:
, w) | g(w) 0, w }. (1.1)
Here, the function (v, w) is dened on the product space Rn