A combined method of regularization and descent along a primal gap (merit) function for solving nonsmooth monotone equilibrium problems is proposed. The same auxiliary uniformly convex function is used for the construction of regularized problems and gap functions. The descent method along a gap function with an inexact line search is applied to solve the regularized problems.

Keywords: nonsmooth monotone equilibrium problem, primal gap function, descent method, inexact line search, uniformly convex function

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