 
Summary: Automation and Remote Control, Vol. 58, N 8, 1997, ñ. 13371347
EVOLVING SYSTEMS
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.
1. INTRODUCTION
It is now generally recognized that a wellfounded 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, nperson 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
