All Solutions of Nonlinear Constrained Systems of Equations

  • Christodoulos A. Floudas
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 37)


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).


Univariate Function Convex Relaxation Convex Envelope Bilinear Term Nonconvex Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Christodoulos A. Floudas
    • 1
  1. 1.Department of Chemical EngineeringPrinceton UniversityPrincetonUSA

Personalised recommendations