Summary: Automation and Remote Control, Vol. 58, N 8, 1997, ñ. 13371347
EQUILIBRIUM PROGRAMMING: GRADIENT METHODS1
A.S. Antipin UDC 517.977.5
Revised 26.07.2004 ã.
The equilibrium programming problem is formulated and its relationship with game for-
mulation is discussed. A forecast method for computing the equilibrium solution is de-
signed and its convergence is proved. The economic interpretation of the initial equilib-
rium problem and its solution are examined.
It is now generally recognized that a well-founded theory underlies the methods of sol-
ving optimization problems, whereas there is no such theory to authenticate the methods
of solving game problems, e.g., saddle problems, n-person games under Nash equilibrium,
inverse optimization problems, and economic equilibrium models.
The need for developing a theory of methods of solving equilibrium problems is obvious,
because precisely these are the problems that describe the ne points underlying the ideas
of compromise between partially (or fully) conicting factors and interests in terms of
models. The methods of solving equilibrium problems are interpreted as mechanisms
for matching conicting factors. In this paper, we examine an equilibrium programming
problem whose solution is a xed point, and design a fairly general approach to computing