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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