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Article
Regularized Extragradient Method of Finding a Solution to an Optimal Control Problem with Inaccurately Specified Input Data
We consider an optimal control problem described by a system of linear ordinary differential equations with boundary conditions of general form defined by inequality-type constraints in the case when the input...
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Article
Extragradient Method for Correction of Inconsistent Linear Programming Problems
For a pair of dual inconsistent linear programming problems, the existence and uniqueness of a correction vector that is optimal in the norm is proved. It is shown that the correction problem is reduced to the...
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Article
Extragradient method for finding a saddle point in a multicriteria problem with dynamics
We consider an optimal control problem for a linear system of ordinary differential equations with an implicitly given boundary condition connected with a multicriteria problem. Such problems arise, for exampl...
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Article
Extragradient method for solving an optimal control problem with implicitly specified boundary conditions
An optimal control problem formulated as a system of linear ordinary differential equations with boundary conditions implicitly specified as a solution to a finite-dimensional minimization problem is considere...
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Article
Regularized extragradient method in multicriteria control problems with inaccurate data
The class of Hilbert space multicriteria optimization problems considered in the paper includes control problems for various dynamical systems with lumped as well as distributed parameters. An equilibrium poin...
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Article
Regularized extraproximal method for finding equilibrium points in two-person saddle-point games
Three variants of the regularized extraproximal method are proposed for finding equilibrium points in two-person saddle-point games. Their convergence is examined, and a regularizing operator is constructed.
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Article
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 ...
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Article
Differential extraproximal 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 prob...
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Article
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 extraproxi...
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Article
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.
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Article
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.
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Article
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...
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Article
Nikolai Alekseevich Izobov (A tribute in honor of his 70th birthday)
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Article
A stabilization method for solution of a parametric multicriteria equilibrium programming problem
A multicriteria equilibrium programming problem comprising a mathematical programming problem as a particular case, a multicriteria Pareto-point search problem, a minimization problem with equilibrium selectio...
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Article
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 Pare...
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Article
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 function...
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Article
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 determ...
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Article
Methods for solving equilibrium programming problems
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Article
Stabilization Method for Unstable Equilibrium Programming Problems with Coupled Constraints
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Article
A Regularized Continuous Extragradient Method of the First Order with a Variable Metric for Problems of Equilibrium Programming
