Trust-region quadratic methods for nonlinear systems of mixed equalities and inequalities

Authors:
Maria Macconi;Benedetta Morini;Margherita Porcelli
Affiliations:
Dipartimento di Energetica “S. Stecco”, Università di Firenze, via C. Lombroso 6/17, 50134 Firenze, Italy;Dipartimento di Energetica “S. Stecco”, Università di Firenze, via C. Lombroso 6/17, 50134 Firenze, Italy;Dipartimento di Matematica “U. Dini”, Università di Firenze, viale Morgagni 67a, 50134 Firenze, Italy
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

Two trust-region methods for systems of mixed nonlinear equalities, general inequalities and simple bounds are proposed. The first method is based on a Gauss-Newton model, the second one is based on a regularized Gauss-Newton model and results to be a Levenberg-Marquardt method. The globalization strategy uses affine scaling matrices arising in bound-constrained optimization. Global convergence results are established and quadratic rate is achieved under an error bound assumption. The numerical efficiency of the new methods is experimentally studied.