问题

Lexicographic Method for Fuzzy Multiobjective Optimization of Structures is presented in this paper.

提出了多目标结构模糊优化的分层序列法，首先把原多目标模糊优化问题分解为一系列单目标模糊优化子问题，该子问题用最大最小法求解。

Illinois,"It is useless to argue about taste and even more useless to litigate it", and that is the case here, the jury has already determined that this is a matter of taste, not matter of law, because they've said there is no libelous speech that nobody could reasonably believe that Hustler was actually suggesting that Jerry Falwell had sex with his mother.

Illinois一案中，您自己曾说过，"争论品味问题是没有意义的，更不要说因此而提起诉讼"，本案陪审团已经认定这是一个品味问题，而不是法律问题，因为他们已经裁定本案没有诽谤的言论，没有一个理性的人会相信，《皮条客》杂志说Jerry Falwell跟他母亲乱交是真的。

All was unexpected. Likin, though, was temporary tax that the Qing Dynasty established for raising money to repress the taiping rebellion. It had been censured for seventy eight years. This showed that the existence of likin had its profound background of economy and society. Abolishing likin was to "change a little, then influence the whole", and it existed contradiction not only between China and other countries, but also between the center and the local authority. The problem of likin systems abolition was the problem about not only economy but also politics.

厘金虽然一开始是清王朝为筹措镇压太平天国运动军费而设立的临时税种，但其屡遭非议却长达78年的历史表明，厘金的存在有其深刻的经济与社会背景，"裁厘"可谓是"牵一发而动全身"，不仅存在着中国与各国列强之间的矛盾，而且存在着中央与地方政权之间的矛盾，厘金的裁撤问题，既是经济问题，又是政治问题。

Illustrations are used to analyze the limitation of line sampling firstly. For linear limit state, the efficiency of LS is affected by the dispersion of the actual important direction from the optimal one, the bigger the dispersion is, the lower the efficiency is. For non-linear limit state, in case that the actual important direction deviates from the optimal one greatly, the efficiency and the precision of LS decrease seriously, even wrong results are obtained.

首先通过算例分析线抽样方法存在的问题，对于线性问题，线抽样法的效率受抽样重要方向与最优重要方向偏离程度的影响，这种偏离程度越大，效率越低；而对于非线性问题，当抽样重要方向与最优重要方向偏离较大时，线抽样的效率和精度均严重下降，甚至得出错误的计算结果。

For the original infinite dimensional problem, if the inexact quasi-newton method with Broyden updating can not converge quickly , for example, it can not attain super linear convergence rate , then when the discretization is becoming finer and finer , we can not get fast convergence rate for the corresponding finite dimensional problem.

对于原来的无限维问题，如果使用不精确Broyden方法不能得到较快的收敛速度，比如超线性收敛性，那么当离散化逐渐加细的时候，对于所得的有限维问题使用不精确Broyden方法也不可能得到较快的收敛速度，所以有必要在无穷维空间上对收敛性问题加以分析，从而为不精确拟牛顿法结合投影法求解算子方程做好准备。

The forth algorithm is the same as the third one with an addition of finite termination criteria. Although the latter two algorithms have only linear rate of convergence, they are especially suitable for large-scale and sparse problems, with features of simple formula, small storage, sparsity preservation and easy implementation.

前者借助NCP函数把互补问题转化为等价的非光滑方程组，再用带参数的光滑方程组近似这些非光滑方程组，最后用牛顿型方法求解所得到的光滑方程组，希望通过光滑参数趋于零得到原来互补问题的解；后者基于等价不动点格式，构造了一个光滑迭代算法和一个具有有限终止性质的算法，虽然这种迭代算法仅有线性收敛速度，但由于其格式简单、存储量小、保稀疏性、非常易于计算机实现等特点，故较适用于求解大规模稀疏问题。

In chapter 3 constructs firstlya new differential merit function by a perturbation structure of VIP and study theproperties of this merit function.Based on this merit function,a continuation-typeNewton method is proposed,which use the technique of inexact linear search forassuring its global convergence,and improves essentially the method of Taji,Fukushima and Ibaraki which can only solve the strong monotone VIP,and has locallyquadratic convergent rate under some condition.

第三章利用变分不等式问题的一种扰动结构构造了新的可微效用函数，并研究了效用函数的性质；在此基础上，给出了一类求解一般单调变分不等式问题的连续型Newton方法CN，方法采用了不精确的线性搜索技术以确保整体收敛性，从本质上改进了Taji、Fukushima和Ibaraki方法只能求解强单调变分不等式问题的局限性，同时又保持了局部二次收敛率。

An optimization method is proposed to solve steady-state optimization problems by linear approximation of the object function and the Linear Matrix Inequalities Problem and Eigenvalue Problem of Linear Matrix Inequalities theory.

提出了将稳态优化问题的目标函数进行线性逼近及用可行性问题求解算法和特征值问题求解算法进行求解的优化方法。

An optimization method is proposed to solved steady-state optimization problems by quadratic approximation of the object function and the Linear Matrix Inequalities Problem and Eigenvalue Problem of Linear Matrix Inequalities theory.

提出了将稳态优化问题的目标函数进行二次逼近及用可行性问题求解算法和特征值问题求解算法进行求解的优化方法。

Thisproblem is changed into the matrix approximation problem with matrix inequalities.Further, it is changed into the generalized eigenvalue problem with linear matrix in-equalities. In addition linear state feedback controller is designed.

先将最优控制问题转化为具有矩阵不等式约束的矩阵逼近问题，又转化为具有线性矩阵不等式约束的矩阵广义特征值最小化问题，从而设计了相应系统的线性状态反馈控制器。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。