For both methods , at most two reduced linear systems of equations with the same coefficient matrix need to be solved in order to get iterative directions at each iteration and the iterative matrix involves only constraints in the working set , whose cardinality are much less than the number of original constraints 在其每次迭论文摘要代中,只有有效工作集中的约束参与计算。在本文中,我们在facchinei一fischer一kanzowkkt点有效约束集识别技术的基础上提出了三个具有强收敛性的qp一free算法。
For example , at each iteration at most four reduced linear systems of equations with the same iterative coefficient matrix need to be solved to get iterative directions and the iterative matrix involves only constraints in the working set , the number of which are much less than that of the original problem 此外它还有其它一些良好性质,例如其子问题通常只包含同系数的线性方程组,并且这些方程组在一定的假设条件下都是可解的。然而,从理论和实用的角度来看,现有的qp一free算法仍存在两个主要问题有待解决。