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A trust-region approach to nonlinear systems of equalities and inequalities. (English) Zbl 0957.65058

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.

MSC:
65K05Mathematical programming (numerical methods)
90C20Quadratic programming
90C51Interior-point methods
90C30Nonlinear programming
65H10Systems of nonlinear equations (numerical methods)