Globally convergent successive approximation method for severely nonsmooth equations

This paper presents a globally convergent successive approximation method for solving F(x) = 0 where F is a continuous function. At each step of the method, F is approximated by a smooth function fk, with ∥fk-F∥→0 as k→∞. The direction -fk′(xk)-1F(xk) is then used in a line search on a sum of squares objective. The approximate function fkcan be constructed for nonsmooth equations arising from variational inequalities, maximal monotone operator problems, nonlinear complementarity problems, and nonsmooth partial differential equations. Numerical examples are given to illustrate the method.