一个解不等式约束非线性规划问题的有效方法

本文提出了一个解不等式约束非线性规划问题有效方法．在这个方法中，考虑解一个等价Ｋｕｈｎ－Ｔｕｃｋｅｒ条件的非线性方程组．这个方程组中ＮＣＰ函数的使用消去了对应于不等式约束的Ｌａｇｒａｎｇｅ乘子的非负性．截断牛顿方法被用来解这个非线性方程组．为了保证全局收敛性，一个强健的损失函数被选为寻查函数，同时方法中插入修正最速下降方向．本文证明了方法的分Ｑ－二阶收敛性，同时指出新方法可以有效地解稀疏大规模非线性规划问题。

A New Efficient Method for Solving Nonlinear Programming Problems with Inequality Constraints

A new efficient method for solving nonlinear programming (NLP) problems is studied in this paper. In this method, a new nonlinear system which is equivalellt to Kuhn-Tucker conditions of the problem is developed. NCP function is used in the nonlinear system such that the nonnegativity of some variables is avoided. The truncated Newton method is used to solve the nonlinear system. In order to guarantee the global convergence, a robust loss function is chosen as a merit function and the steepest method inserted is used to descrease the merit function. The Q-quadratical convergence is proved and the theoretical results show that the new method is efficient for solving NLP problems.