Abstract: There exists an optimization problem in management,engineering design,scientific research,and other aspects of military command generally. But in the actual situation most of these issues are summarized in the nonlinear programming problem. As carry equality and inequality constraints complicated cases, theoptimization problem solving has always been more complicated, and difficult.Under appropriate conditions, NCP Function can be combined with constrained optimization problem, NCP function of unconstrained minimization solution corresponds to the solution of the original constrained problem and its corresponding multiplier. In this paper, a new class of NCP function is proposed for the minimization conditions,We prove 1-1 corresponding relationship of optimality solution between the primal constrained problem and the new unconstrained problem.Meanwhile, Lagrangian multiplier method corresponding with new augmented Lagrangian function is proposed.And this method is implementable and convergent.

Key words: nonlinear programming, NCP function, multiplierLagrangian function, convergent

摘要： 在经营管理、工程设计、科学研究、军事指挥等方面普遍存在着最优化问题,而实际问题中出现的绝大多数问题都被归纳为非线性规划问题之中。作为带等式、不等式约束的复杂事例,最优化问题的求解向来较为繁琐、困难。适当条件下,非线性互补函数(NCP)可以与约束优化问题相结合,其中NCP函数的无约束极小解对应原约束问题的解及其乘子。本文提出了一类新的NCP函数用于解决等式和不等式约束非线性规划问题,结合新的NCP函数构造了增广Lagrangian函数。在适当假设条件下,证明了增广Lagrangian函数与原问题的解之间的一一对应关系。同时构造了相应算法,并证明了该算法的收敛性和有效性。

关键词: 非线性规划, NCP函数, 乘子Lagrangian函数, 收敛性