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The Levenberg–Marquardt method is a fundamental regularization technique for the Newton method applied to nonlinear equations, possibly constrained, and possibly with singular or even nonisolated solutions. We review the literature on the subject, ...

It is well-recognized that in the presence of singular (and in particular nonisolated) solutions of unconstrained or constrained smooth nonlinear equations, the existence of critical solutions has a crucial impact on the behavior of various Newton-...

The Wigner equation describing stationary quantum transport has a singularity at the point $k=0$. Deterministic solution methods usually deal with the singularity by just avoiding that point in the mesh (e.g., Frensley’s method). Results from such ...

For constrained equations with nonisolated solutions, we show that if the equation mapping is 2-regular at a given solution with respect to a direction in the null space of the Jacobian, and this direction is interior feasible, then there is an ...

The LP-Newton method for constrained equations, introduced some years ago, has powerful properties of local superlinear convergence, covering both possibly nonisolated solutions and possibly nonsmooth equation mappings. A related globally convergent ...

The projected Levenberg-Marquardt method for the solution of a system of equations with convex constraints is known to converge locally quadratically to a possibly nonisolated solution if a certain error bound condition holds. This condition turns out ...

We consider the mathematical program with vertical complementarity constraints. We show that the min-max-min problems and the problems with max-min constraints can be reformulated as the above problem. As a complement of the work of Scheel and Scholtes ...

The purpose of this paper is to present a new family of numerical methods for the approximation of second order hyperbolic partial differential equations submitted to a convex constraint on the solution. The main application is dynamic contact problems. ...