Dennis, J. E. jun.; El-Alem, Mahmoud; Williamson, Karen A trust-region approach to nonlinear systems of equalities and inequalities. (English) Zbl 0957.65058 SIAM J. Optim. 9, No. 2, 291-315 (1999). 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.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.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. Reviewer: Klaus Schittkowski (Bayreuth) Cited in 24 Documents MSC: 65K05 Numerical mathematical programming methods 90C20 Quadratic programming 90C51 Interior-point methods 90C30 Nonlinear programming 65H10 Numerical computation of solutions to systems of equations 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 Software:CDFCOR; LANCELOT; LAPACK PDFBibTeX XMLCite \textit{J. E. Dennis jun.} et al., SIAM J. Optim. 9, No. 2, 291--315 (1999; Zbl 0957.65058) Full Text: DOI