含弱互补函数的可行的无子规划算法

A QP-Free Feasible Method with Slack NCP Function

用弱互补函数来代替F-B互补函数,由此而构建出四个光滑的线性方程.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.采用修改的拟牛顿算法修正,在没有要求子矩阵Hk是一致正定的条件下,证明该算法具有全局收敛性和局部超线性收敛性.算例表明,该算法具有很好的应用前景.

A slack nonlinear complementarity problem （NCP） function is used to replace the F-B NCP function, and the second linear system is modified to ensure the descent of the search direction and the feasibility of the iteration. 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. It is also proved that the method has super linear convergence rate. Some preliminary numerical results indicate that this new QP-free feasible method is of promising feasibility.