F. P. Vasil’ev

Extraproximal method for solving two-person saddle-point games

An equilibrium model is proposed for a two-person saddle-point game with partially coincident or conflicting interests. Meaningful interpretations of such a game are discussed. Three variants of the extraproximal method for finding an equilibrium point are proposed, and their convergence is proved.

Multicriteria equilibrium programming: Extragradient method

Multicriteria equilibrium programming includes as its particular cases mathematical programming, saddle point calculation, the multicriteria search for Pareto solutions, minimization with an equilibrium choice of the feasible set, etc. An extragradient method is proposed for the numerical solution of the multicriteria equilibrium programming problem, and the convergence of this method is examined.

A regularized Newton method for solving equilibrium programming problems with an inexactly specified set

Unstable equilibrium problems are examined in which the objective function and the set where the equilibrium point is sought are specified inexactly. A regularized Newton method, combined with penalty functions, is proposed for solving such problems, and its convergence is analyzed. A regularizing operator is constructed.

Regularized extragradient method for finding a saddle point in an optimal control problem

We propose a regularized variant of the extragradient method of saddle point search for a convex-concave functional defined on solutions of control systems of linear ordinary differential equations. We assume that the input data of the problem are given inaccurately. Since the problem under consideration is, generally speaking, unstable under a disturbance in the input data, we propose a regularized variant of the extragradient method, investigate its convergence, and construct a regularizing operator. The regularization parameters of the method agree asymptotically with the disturbance level of the input data.

Regularized extragradient method for solving parametric multicriteria equilibrium programming problem

A regularized extragradient method is designed for solving unstable multicriteria equilibrium programming problems. The convergence of the method is investigated, and a regularizing operator is constructed.

Continuous extragradient method for a parametric multicriteria equilibrium programming problem

We consider a multicriteria equilibrium programming problem including, as special cases, the mathematical programming problem, the problem of finding a saddle point, the multicriteria problem of finding a Pareto point, the minimization problem with an equilibrium choice of an admissible set, etc. We suggest a continuous version of the extragradient method with prediction and analyze its convergence.

On the convergence rate of the continuous version of the regularized gradient method

In this paper the convergence rate of the gradient type iterative regularization is given in the case when the convex mathematical programming problems additionally satisfy the condition of the normal regularity and the method is described in its continuous variant. The dependence of the convergence rate on the penalty and regularization parameters, on the stepsize and on the accuracity in the basic informations in formulated.

Differential extragradient method for finding an equilibrium in two-person saddle-point games

We describe an equilibrium model of a two-person saddle-point game with partially opposite or coinciding interests. To find an equilibrium point, we suggest an extraproximal method in the form of a Cauchy problem for a system of ordinary differential equations with prediction. We consider three versions of this method and analyze their convergence.

Regularized continuous extragradient method for a multicriterial equilibrium programming problem

For solving unstable multicriterial problems, we suggest a regularized version of the continuous extragradient method, analyze its convergence, and construct a regularizing operator.

Methods for solving unstable equilibrium programming problems with coupled variables

Regularization (stabilization, residual and quasisolution) methods for solving an unstable equilibrium programming problem are proposed for the case when not only the objective function but also the set determined by coupled inequality constraints are given inexactly. The convergence of these methods is studied. A regularizing operator is constructed.