Pseudotransient Continuation for Solving Systems of Nonsmooth Equations with Inequality Constraints

This paper investigates a pseudotransient continuation algorithm for solving a system of nonsmooth equations with inequality constraints. We first transform the inequality constrained system of nonlinear equations to an augmented nonsmooth system, and then employ the pseudotransient continuation algorithm for solving the corresponding augmented nonsmooth system. The method gets its global convergence properties from the dynamics, and inherits its local convergence properties from the semismooth Newton method. Finally, we illustrate the behavior of our approach by some numerical experiments.