Extension of Newton's Method to Mixed Systems of Nonlinear Equations and Inequalities.
Abstract
The paper shows how Newton's method may be extended, by using linear programming, to solve mixed systems of nonlinear equations and inequalities of the form g(x) < or = 0, f(x) = 0. The number of equations and/or inequalities need not equal the number of variables, and the solutions need not be unique or isolated. An extension of the Kantorovich theorem is proved for this method; it shows, among other things, that the same quadratic rate of convergence holds for this technique as for the conventional version of Newton's method. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1971
- Accession Number
- AD0732054
Entities
People
- Stephen M. Robinson
Organizations
- University of Wisconsin–Madison