A Trust-Region-Algorithm For Recursive Quadratic Progoamming

Recursive quadratic programming is a family of techniques developed by Bartholo- mew-Biggs and other authors for solving nonliner programming problems.The method is based on the first-order optimalitycinditions for a local minimizer of the augmented Lagrangian,with different form,being transformed into another nonliner system. Then the nonliner system can be solved easily by existed techniques,such as Newton-like e.c. Trust region algorithm is another efficent technique for the nonliner programming problems.The technique employs a more fitable mode for f(x) as objective function ,and solve it in a trust region. It doesn抰 need search for the steo length which depends on a line search technique. In this paper, the recursive quadratic programming (RQP) putforwarded byJ.M.Martire and L.T.Santos(1998) and the region algorithm is used together for solving the equality constrained optimization. The new algorithm intro- duces a new parameter which not only improves the shortcoming in the two methods but also keep the good. In this paper , the V2L, V2c(x) are not neccessory,In the section 3 global convergence and local superlinear convergence results are proved.Some numerical experiments suggset practical efficiency of the method.