| The constrained nonlinear programming problems(CNLP) is a very important component part in operations research.It has wide application in natural science, en-gineering and economics. In recent years, the method that a local minimum of CNLP is obtained by solving KKT-systems for CNLP becomes one of the efficient numerical methods for CNLP. The main idea of the method is to reformulate the KKT-systems for CNLP as an unconstrained (or simply constrained) smooth minimization problem equivalently. Then a KKT-point for CNLP is obtained by using classical numerical methods for the problem. In this thesis, enlightened by the idea, author equivalently transformed the KKT-systems for CNLP into some new simply constrained smooth minimization problems different from that in literature. The details arc as follows:1.Firstly.author constructed a new NCP-function that is only defined in first quad-rant, then equivalently reformulated the KKT-systems for CNLP as a smooth mini-mization problem with non-negative constraints. As in the infeasible method for non-linear complementarity problem, an additional variable was introduced in order to getting simple constraints- An efficient trust region algorithm for solving KKT point for CNLP was provided via using the method proposed by Qi etc[15]. The global convergence and local superlinear (or quadratic) convergence for the algorithm were shown under suitable conditions.2. Futhermorc. a new method that to construct NCP-functions was proposed. By using the method, author obtained a new NCP-function with many useful properties, such as Lipschitz continuity. Strong semismoothness. good coercivity etc. A new refor-mulation was constructed by using it, and a similar algorithm as above was provided on the reformulation- The global convergence and local superlinear (or quadratic) con-vergence were obtained under weaker assumptions than above. Numerical results show that the algorithm is robust and efficient.
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