一类新的乘子方法

提出一种乘子方法用于解带不等式约束的非线性规划问题。其具体思路如下：先将原不等式约束问题用Fischer-Burmeister非线性规划互补（NCP）函数转化为一个等价的等式约束问题；在此基础上，经过适当修改后的DI PILLO的方法以及参考Xuewu Du，Liansheng Zhang，Yuelin Gao的方法，将等式约束问题转化为无约束极小化问题。在适当的假定条件下，通过求解一个无约束连续可微函数的最小值来得到原约束问题的解，从而可以使用标准的无约束极小化方法来求其解。最后，讨论了原不等式约束问题和转换后的无约束问题相关的最优性条件之间的等价关系，以及局部最优性和全局最优性结果：即在适当的假设下，只要罚参数充分大，并不要求罚参数趋于无穷，则原约束问题的最优解（或KKT点）对应于增广Lagrangian函数的最优解（或平稳点）。

A New Multipliers Algorithm

In this paper, a new multipliers algorithm is introduced for solving nonlinear programming problems with inequality constraints. The relevant feature of the proposed approach is that, the primal problem with inequality constrains can be changed to one with equality constrains by using the Fischer-Burmeister NCP function at first, then, we can change the latter to an unconstrained minimization problem. So that standard unconstrained minimization techniques can be employed to the original constrained problem with inequalities. Finally, the equivalence between the primal problem and the converted one is also discussed in this paper, i.e., under suitable hypotheses and for sufficiently large values of the penalty parameters but without requiring the penalty parameters go to infinity, every minimum point （KKT point） of the original constrained problem corresponds to a minimum point （stationary point） of an augmented Lagrangian on the product space of problem variables and multipliers.