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 Num. Meth. Prog., 2002, Volume 3, Issue 1, Pages 211–221 (Mi vmp754)

A regularized first-order continuous extragradient method with variable metric for solving the problems of equilibrium programming with an inexact set

A. S. Antipina, B. A. Budakb, F. P. Vasil'evb

a Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
b Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: A regularized continuous variant of the gradient projection method with prediction in combination with the penalty function method in a space of variable metric is proposed for solving the problems of equilibrium programming. The convergence of a trajectory started at an arbitrary initial point to the normal solution of the problem is proved. A regularizing operator is found.

Keywords: extragradient methods, equilibrium programming, inexact sets, gradient projection method, penalty function method, spaces of variable metric.

Full text: PDF file (168 kB)
UDC: 517.988.68:519.85

Citation: A. S. Antipin, B. A. Budak, F. P. Vasil'ev, “A regularized first-order continuous extragradient method with variable metric for solving the problems of equilibrium programming with an inexact set”, Num. Meth. Prog., 3:1 (2002), 211–221

Citation in format AMSBIB
\Bibitem{AntBudVas02} \by A.~S.~Antipin, B.~A.~Budak, F.~P.~Vasil'ev \paper A regularized first-order continuous extragradient method with variable metric for solving the problems of equilibrium programming with an inexact set \jour Num. Meth. Prog. \yr 2002 \vol 3 \issue 1 \pages 211--221 \mathnet{http://mi.mathnet.ru/vmp754}