Extragradient methods for nonsmooth equilibrium problems in Banach spaces

عنوان به زبان ديگر

پديدآورندگان

N. Iusem Alfredo iusp@impa.br IMPA, Brazil , Mohebbi Vahid mohebbi@impa.br, mohebbimath@gmail.com IMPA, Brazil

تعداد صفحه

6

كليدواژه

Armijo linesearch , equilibrium problem , extragradient method , Halpern regulariza , tion , pseudomonotone bifunction.

سال انتشار

1397

عنوان كنفرانس

چهارمين كنفرانس بين المللي آناليز غير خطي و بهينه سازي

زبان مدرك

انگليسي

چكيده فارسي

We introduce and analyze the extragradient method for solving nonsmooth equilibrium prob- lems in Banach spaces, which generalizes the extragradient method for variational inequalities. We prove weak convergence of the generated sequence to a solution of the equilibrium problem, under standard assumptions on the bifunction which defines the problem, akin to those required in the convergence analysis of the method, when applied to solving variational inequalities. Then, we propose a regularization procedure which ensures strong convergence of the generated sequence to a solution of the problem.

چكيده لاتين

We introduce and analyze the extragradient method for solving nonsmooth equilibrium prob- lems in Banach spaces, which generalizes the extragradient method for variational inequalities. We prove weak convergence of the generated sequence to a solution of the equilibrium problem, under standard assumptions on the bifunction which defines the problem, akin to those required in the convergence analysis of the method, when applied to solving variational inequalities. Then, we propose a regularization procedure which ensures strong convergence of the generated sequence to a solution of the problem.

كشور

ايران