Nonlinear Global Optimization Using Interval Arithmetic and Constraint Propagation 
 Abstract  We consider the problem of finding the global optimum, and the corresponding set of optimal points, of a nonlinear function f over a compact right parallelepiped D parallel to the coordinate axes. A new branchandbound type method is described. The method is an extension of the classical interval global optimization method originally given by Moore and Skelboe which iteratively investigates subboxes of D using monotonicity tests and interval Newton methods for reducing the set guaranteed to contain all solutions. The extension described uses constraint propagation (CP) in each iteration to further reduce this set, without losing solutions. This is done by applying CP for finding rigorous bounds for the set of stationary points, i.e., enclosing the solutions to the nonlinear set of equations f'(x)=0.  Keywords  Global optimization, interval analysis, constraint propagation.  Type  Book [Chapter]  Editors  Models and Algorithms for Global Optimization  Year  2007 Vol. 4 pp. 4558  Publisher  Springer Verlag  Series  Springer Optimization and Its Applications  ISBN / ISSN  13: 9780387367200  Electronic version(s)  [pdf]  BibTeX data  [bibtex]  IMM Group(s)  Scientific Computing 
