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Zbl 0957.65058
Dennis, J.E.jun.; El-Alem, Mahmoud; Williamson, Karen
A trust-region approach to nonlinear systems of equalities and inequalities. (English)
[J] SIAM J. Optim. 9, No.2, 291-315 (1999). ISSN 1052-6234; ISSN 1095-7189/e

Authors' abstract: Two new trust-region algorithm for the numerical solution of systems of nonlinear equalities and inequalities are introduced. The formulation is free of arbitrary parameters and possesses sufficient smoothness to exploit the robustness of the trust-region approach. The proposed algorithms are one-sided least-squares trust-region algorithms. The first algorithm is a single-model algorithm, and the second one is a multimodel algorithm where the Cauchy point computation is a model selection procedure.\par Global convergence analysis for the two algorithms is presented. Our analysis generalizes to systems of nonlinear equalities and inequalities the well-developed theory for nonlinear least-squares problems.\par Numerical experiments on the two algorithms are also presented. The performance of the two algorithm is reported. The numerical results validate the effectiveness of our approach.
[Klaus Schittkowski (Bayreuth)]
MSC 2000:
*65K05 Mathematical programming (numerical methods)
90C20 Quadratic programming
90C51 Interior-point methods
90C30 Nonlinear programming
65H10 Systems of nonlinear equations (numerical methods)

Keywords: fraction of Cauchy decrease; global convergence; multimodel algorithm; nonlinear least squares; one-sided least squares; trust-region methods; active-set strategies; numerical examples; systems of nonlinear equations; systems of nonlinear inequalities; convergence

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