An approximate method for solving the convex programming problem

We consider an iterative process for maximization of a convex nondifferentiable functional in a real Hilbert space. Two-sided bounds on the optimal functional value are derived. Stability of the approximate solutions is considered. Convergence of the proposed iterative process is proved.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 122–129, 1986