A Gauss–Newton method for solving bound-constrained underdetermined nonlinear systems

Abstract

An iterative method for solving bound-constrained underdetermined nonlinear systems is presented. The procedure consists of a Gauss--Newton method embedded into a trust–region strategy. Global and fast local convergence results are established. A specific implementation of the method is given along with its application to nonlinear systems of equalities and inequalities.

Keywords:

• underdetermined nonlinear systems
• simple bounds
• trust-region methods
• global convergence
• quadratic convergence

Acknowledgements

This work was supported by MIUR, Roma, Italia, through PRIN 2007 ‘Progetti di Ricerca Interesse Nazionale’, INDAM-GNCS, Italy.