Observing that the newton direction is always a descent direction of the square norm of the gradient , even if it is not a descent direction of the objective function , which will result some linear research - such as armijo research or wolfe research - fail 因此，该算法是颇受欢迎的算法之一。然而，若问题的目标函数的hessian阵不正定，则不能保证算法产生的方向是目标函数的下降方向。
3 ) evolves perona - malik equation to the form of weighted smoothing in two orthogonal directions . brings hessian method , which is an approach to extract the image feature direction , into the technology of smoothing image 3 )推导perona ? malik方程为在相互垂直方向不同程度平滑的形式，将提木于柿微分方程的图街个滑技术及其应用研穴摘要取图像特征方向的hessain方法应用到图像平滑技术中。
However , some of them are restrictive . for some of these methods , the convergence is not known in this paper , based on a modified bfgs update formula proposed by li and fukushima , we propose a modified bfgs method for solving equality constrained optimization 本文在li - fukushima提出的求解无约束问题的修正bfgs公式的基础上，对求解等式约束问题的sqp算法，提出一个保证qp子问题的目标函数的hessian阵的正定性的修正方案。
It is proven that these modified dual algorithms still have the same convergence results as those of the conceptional dual algorithms in chapter 2 and chapter 3 . secondly , a dual algorithm is constructed for general constrained nonlinear programming problems and the local convergence theorem is established accordingly . the condition number of modified lagrange function ' s hessian is estimated , which also depends on the penalty parameter 证明这些修正的对偶算法仍具有同前两章的概念性对偶算法相同的收敛性结果，我们还进一步构造了一般约束非线性规划问题的对偶算法，建立了相应的局部收敛理论，最后估计了修正lagrange函数的hesse阵的条件数，它同样依赖于罚参数。
Nobody came near them , and their movements showed a mechanical regularity ; their forms standing enshrouded in hessian wroppers - sleeved brown pinafores , tied behind to the bottom , to keep their gowns from blowing about - scant skirts revealing boots that reached high up the ankles , and yellow sheepskin gloves with gauntlets . the pensive character which the curtained hood lent to their bent heads would have reminded the observer of some early italian conception of the two marys 没有人走近她们她们的动作像机械一样地一致她们站在那儿，身上裹着麻布罩衫这是一种带袖子的黄色围裙，从背后一直扣到下摆，免得让风吹来吹去穿着短裙，短裙下面是脚上穿的靴子，靴子的高度到达了脚踝以上，手上戴的是带有护腕的羊皮手套。
In the second part , a decomposition method for solving semidefmite quadratic programming with box constraints is proposed . a regular splitting of the hessian matrix of the problem is used in the algorithm . the convergence of the algorithm is proved under certain assumptions , the numerical results are also given 第二部分把解边界约束正定二次规划问题的正则分解算法推广到求解边界约束半正定二次规划问题，在理论证明的基础上还进行数值检验，结果说明算法是有效的。
At the windows of the houses men could be seen in military coats and hessian boots , laughing and strolling through the rooms . in the cellars , in the storerooms similar men were busily looking after the provisions ; in the courtyards they were unlocking or breaking open the doors of sheds and stables ; in the kitchens they were making up fires , and with bare arms mixing , kneading , and baking , and frightening , or trying to coax and amuse , women and children 房屋的窗户里，闪现着穿军大衣和短靴的人们，他们嘻笑着出入于各个房间在地窖和地下室里，这些人喧宾夺主地款待自己在院子里，这些人打开或砸开披屋和马厩的门在厨房，则点燃炉灶，卷起袖子和面，烘烤和煎炸，恐吓，调笑和爱抚妇女和儿童。
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。
The results of numerical experiment are reported to show the effectiveness of the proposed algorithms . reduced hessian algorithm has became one of the very popular and most effecive methods for solving nonlinear equality constrained programming . recently , chaya gur - witz proposed the two - piece update of a projected hessian matrix 最近， chayagurwitz在nocedal和overton等人工作的基础上，提出了两块校正的投影hesse矩阵方法，讨论了其算法的局部收敛速率，但未涉及整体收敛性。
A dual algorithm , based on an exponential potential function , is proven to be included in this class of dual algorithms . detailed convergence results for the dual algorithm are given and the estimate of the condition number of the potential function ' s hessian is established , which depends on the penalty parameter . 2 还基于一个指数型势函数建立了相应的对偶算法，它也属于这类对偶算法，对这一对偶算法，给出了精细的收敛性结果，同时估计了势函数的hesse阵的条件数，它依赖于罚参数。
