Engineering Applications of the Chow-Yorke Algorithm

The Chow-Yorke algorithm is a scheme for developing homotopy methods that are globally convergent with probability one. Homotopy maps leading to globally convergent algorithms have been created for Brouwer fixed point problems, certain classes of nonlinear systems of equations, the nonlinear complementarity problem, some nonlinear two-point boundary value problems, and convex optimization problems. The Chow-Yorke algorithm has been successfully applied to a wide range of engineering problems, particularly those for which quasi-Newton and locally convergent iterative techniques are inadequate. Some of those engineering applications are surveyed here.