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We study the convergence of the projected subgradient method for constrained convex optimization in a Hilbert space. Our goal is to obtain an ε-approximate solution of the problem in the presence of computational errors, where ε is a given positive number. The results that we obtain are important in practice because computations always introduce numerical errors. [ABSTRACT FROM AUTHOR]

In this article, we discuss a nondifferentiable nonlinear penalty method for an optimization problem with inequality constraints. A smoothing method is proposed for the nonsmooth nonlinear penalty function. Error estimations are obtained among the optimal value of smoothed penalty problem, the optimal value of the nonsmooth nonlinear penalty optimization problem and that of the original constrained optimization problem. We give an algorithm for the constrained optimization problem based on the smoothed nonlinear penalty method and prove the convergence of the algorithm. The efficiency of the smoothed nonlinear penalty method is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]