Extragradient method for searching for an equilibrium point in two-person saddle-point games

Regularized extragradient method for searching for an equilibrium point in two-person saddle-point games

“…It was proved in [6] that every saddle point is a solution (an equilibrium point) of game (1)- (4). Under the assumption that exact input data , , and are given, various variants of the extra proximal and extragradient methods for finding a saddle point of this game were proposed in [1][2][3][4][5][6].…”

“…Let a point , where and , satisfy the inequalities (6) Then it is called a saddle point of function (5). The set of all saddle points is denoted by .…”

“…Under the assumption that exact input data , , and are given, various variants of the extra proximal and extragradient methods for finding a saddle point of this game were proposed in [1][2][3][4][5][6]. How ever, in practice, the input data usually contain errors.…”

“…In order to reliably find solutions of desired accuracy to unstable prob lems, special methods called regularization methods are required (see [7][8][9][10][11]). Below, we propose and examine regularized variants of the extragradient method introduced in [6].…”

“…As shown in [1][2][3][4][5][6], problem (1)-(4) is a mathematical model of the two person saddle point game. For instance, it describes the behavior of a borrower and a creditor on the credit market or the interaction of two production units for which the production of each unit can be a resource (raw material) for the other.…”