Tong, Xiaojiao A trust region algorithm for nonlinear problems of equalities and inequalities. (English. Chinese original) Zbl 0984.65060 Chin. J. Numer. Math. Appl. 23, No. 3, 90-102 (2001); translation from J. Numer. Methods Comput. Appl. 22, No. 1, 53-62 (2001). Summary: This paper presents a trust region algorithm for nonlinear problems of equalities and inequalities. The proposed problem is changed to a least-squares problem with nonnegative constraints by using slack variables. An equivalent KKT condition is derived, which is a basis of constructing the new algorithm. The global convergence is established under general conditions and a local quadratic convergence is proved for nondegenerate point satisfying second-order sufficient conditions. Numerical tests for our algorithm are also given. MSC: 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming 90C55 Methods of successive quadratic programming type Keywords:numerical tests; trust region algorithm; least-squares problem; KKT condition; global convergence; local quadratic convergence PDFBibTeX XML