| 1. | We also show that the unit steplength is essentially accepted
并证明算法的全局收敛性和超线性收敛性。 |
| 2. | Under mild conditions , we prove the global and superlinear convergence of the method
在较弱的条件下，得到了算法的全局收敛性及其超线性收敛性。 |
| 3. | Using the comparison principle , it is proved that the proposed method is of superlinear convergence
利用比较原理，间接证明该算法是一种具有超线性收敛性的近似牛顿法。 |
| 4. | Moreover , we show that if the second order sufficient conditions holds at a solution of the problem , then the method is 2 - step superlinearly convergent
而且，我们证明：若在问题的解处二阶充分条件成立，则相应的sqp算法具有2步超线性收敛性。 |
| 5. | Lc1 unconstrained optimization problem was discussed in the second chapter , giving a new trust region method and proving its global convergence and superlinear convergence under some mild conditions
给出了一个新的信赖域算法，并在一定的条件下证明了算法的全局收敛性和局部超线性收敛性。 |
| 6. | Under mild conditions , we prove that the proposed method is globally convergent . moreover , we show that after finite iterations , the unit step is always accepted , and the method locally reduces to the modified bfgs method
在较弱的条件下，我们证明所提出的方法具有全局收敛性，此外，本文证明在有限次迭代后，单位步长总是可接受的，因此，算法还原为mbfgs法，从而这种方法具有局部超线性收敛性。 |
| 7. | It exploits the structured of the hessian matrix of the objective function sufficiently . an attractive property of the structured bfgs method is its local superlinear / quadratic convergence property for the nonzero / zero residual problems . the local convergence of the structured bfgs method has been well established
它们充分利用了目标函数的hesse矩阵的结构以提高算法的效率，该算法的显著优点是对于零残量问题具有二阶收敛性而对于非零残量问题具有超线性收敛性。 |
| 8. | In the third chapter we discuss lc1 constrained optimization problem . to solve it , we turn it into nonsmooth equations , utilizing inexact theory we give an inexact generalized newton ' s method and under some mild conditions we prove that it is global convergence and superlinear convergence
首先将其约束问题的求解转化为非光滑方程组的求解，然后利用不完全求解理论给出了一个非精确的广义牛顿算法，在一定的条件下证明了算法的全局收敛性和局部超线性收敛性并给出了lc ~ 1非线性约束问题的收敛性条件。 |
| 9. | Because three systems of equations solved at each iteration have the same coefficients , so the ammount of computation are less than that of the existing sqp algorithms . under some common conditions ( such as the second order sufficient condition ) which are used in some references , we prove that the algorithm possesses not only global convergence , but also strong convergence and superlinear convergence
该算法在每次迭代时所需解的三个线性方程组具有相同的系数，因此计算量要比现有的sqp方法有所减少；在与一些文献平行的假设条件(如二阶充分条件)下，论文证明了算法不仅具有全局收敛性，而且还具有强收敛性和超线性收敛性 |
