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In this article, we consider the problem of finding a solution of a nonsmooth constrained (and not necessarily square) system of equations. We first reformulate the original problem as an equivalent system of equations with nonnegative constraints, and then present a smoothing projected Levenberg-Marquardt type algorithm to solve the reformulated system, which solves a strictly convex quadratic program at each iteration. We show that this algorithm not only converges globally, but also converges locally superlinearly under an error bound assumption that is much weaker than the standard nonsingularity condition. Some numerical results for the presented algorithm indicate that the algorithm works quite well in practice. [ABSTRACT FROM PUBLISHER]

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]