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Computational Mathematics and Mathematical Physics. Vol. 37. No. 11, 1997, pp. 1285 1296. Translated from Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki.
 

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
A.S. Antipin
Moscow, Russia
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
point v #
## # that satises the following extremal inclusion with functional constraints:
v # # Argmin{#(v # , w) | g(w) # 0, w
## }. (1.1)
Here, the function #(v, w) is dened on the product space R n
R n ,
and# # R n is a

  

Source: Antipin, Anatoly S. - Dorodnicyn Computing Centre of the Russian Academy of Sciences

 

Collections: Computer Technologies and Information Sciences; Mathematics