A New Simplicial Approximation Algorithm With Restarts: Relations Between Convergence and Labelings

Abstract

A simplicial approximation algorithm is presented which is applicable to the fixed point problem in Rn or in Rn+, the nonlinear complementarity problem, and the problem of solving a system of nonlinear equations in Rn. The algorithm employs a variable initial point, admits a restart procedure, and uses a broad class of matrix labels. This generality yields convergence and existence results under rather weak assumptions. Examples are presented which emphasize relations between labelings and convergence, and illustrate the potential for solving nonlinear equations when Newton's method fails.