Introduction to Optimum Design, 2nd Edition

Appendix C A Numerical Method for Solution of Nonlinear Equations

Nonlinear equations are encountered in many fields of engineering. In design optimization, such equations arise when we write the necessary conditions of optimality for unconstrained or constrained problems, discussed in Chapter 4. Roots of that nonlinear set of equations are the candidate minimum designs. Thus the problem of finding roots of nonlinear equations must be treated.

The analytical solution of nonlinear equations is almost impossible except in very simple cases where elimination of variables can be carried out. Therefore, numerical methods and digital computers must be used to find the solutions of such systems. In this appendix, we describe a basic numerical method ...