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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 give an existence result to a class of evolutionary quasi-variational inequalities with adaptive set of feasible solutions, where the adaptivity is modeled by solution-dependent equality constraints. A fundamental role will be played by the concept of Mosco convergence related to set-valued applications. Finally, we apply our achievements to the dynamic multiclass network equilibrium problem and provide a numerical example. [ABSTRACT FROM AUTHOR]

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]