All Solutions of Nonlinear Constrained Systems of Equations

Abstract

In this chapter, we discuss the enclosure of all solutions of nonlinear constrained systems of equations. Section 23.1 provides the motivation from the applications’ point of view and reviews briefly the major previous approaches. Section 23.2 defines the problem and presents the key elements of the global optimization approach. Section 23.3 discusses several theoretical results for the convex lower bounding problems. Section 23.4 presents the global optimization based algorithmic approach for enclosing all solutions of constrained systems of equations. Finally, section 23.5 presents several computational studies on problems taken from the literature. The material presented in this chapter is based on the work of Maranas and Floudas (1995).