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中文摘要：
D．G．PU（2004）提出了一类解不等式约束的最优化问题的QP-free方法，所有得到的迭代点均为可行点。这方法是利用了非线性的Fischer-Burmeiser互补函数，在满足KKT条件的基础上，构建出的几个非光滑线性方程组。但Fischer-Burmeister函数在原点是不可微的，使得构建出的方程组是半光滑的。为此，提出一个修正的光滑化的F-B函数，由它而构建出的方程组是光滑的；还修改了第二个线性方程，从而保证了迭代点的可行性和目标函数的下降性；在一些较弱的条件下，证明了算法具有收敛性和局部超线性收敛性；通过一些算例的计算表明，算法具有很好的应用前景。
英文摘要：
D.G. PU （2004） proposed a new QP-free method for the minimization of a smooth function subject to smooth inequality constraints, which ensured the feasibility of all iterates. The method is based on a nonsmooth equation reformulation of the KKT optimality conditions, by using the Fischer-Burmeiser nonlinear complementarity problem function. Revised NCP function instead of the F-B NCP function and modify the second linear system to en- sure the descent of the search direction and the feasibility of the iteration are used. The method is based on a smooth equation reformulation of the KKT optimality condition. In particular, this method is globally convergent without assuming the uniformly positive definiteness of the submatrix obtained by the Newton or Quasi Newton method. The method has superlinear convergence rate also proved. Some preliminary numerical results indicate that this new QP-free feasible is quite promising.
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