线性优化

In chapter 4, a sufficient condition for stability of time-delay T-S fuzzy systems subject to actuator saturation is first provided, and the problem of estimating the domain of attraction is also formulated.

第四章针对输入受约束的时滞T-S模糊系统，在系统参数确定的情况下，给出系统渐近稳定的充分条件，系统的吸引域的估计问题被转化为一个线性矩阵不等式形式的约束优化问题。

Based on the stability condition, the robust stability of uncertain time-delay T-S fuzzy systems subject to actuator saturation is discussed, and the state feedback gain that maximizes the domain of attraction is designed.In chapter 5, a problem of determing stability domain of time-delay T-S fuzzy systems with input saturation is discussed.

在系统参数不确定的情况下，通过构造适当的Lyapunov-Krasovskii泛函，同样给出了该不确定系统的鲁棒稳定性条件，通过求解线性矩阵不等式形式的约束优化问题，可以得到使吸引域尽可能大的状态反馈增益。

At the same time,the I_ calculated according to ven den Dool's definition will be of poor comparability since retention temp. TR and carbon number n of n-alkanes is not linearly correlated, especially when ...

根据恒温与线性程升的保留值方程建立的各种柱温模式下的保留指数相互转换方法能准确快速地预测不同柱温模式下的保留指数，以此来建立通用数据库以适应不同的分析条件的需要，特别是从2种升温模式出发预测其它柱温模式下的保留值能更方便地对复杂样品的分离条件进行优化。

This paper addresses problems in linear quadratic optimal control of EHT transmission line.

本文论证了超高压输电线路线性二次优化控制的若干问题。

The numercial simulation has been carried out, and the experimental results show that this method has been improved significantly comparing with the traditional one in nonlinear optics. Secondly, a second order system of semilinear elliptic equations, which comes from a mathematics model of the electric potential distribution of a media surrounded with the protein, is transformed into a variational problem, the existence of solution of it is proved by using variational principle and Trudinger—Moser inequality, and the relation between the solutions of variational problem and the solutions of its dual problem is obtained.

首先，讨论了非线性光学中的二次谐波产生的耦合方程组，利用变分法证明了耦合方程组非平凡解的存在性，然后进行了数值模拟，实验结果表明文中方法比经典的非线性光学中的方法有较大的改进，这对优化光倍频器件的设计将有所帮助；其次，将一类二阶半线性椭圆型方程组转化为一个变分问题，然后利用变分法和

Since any equality constraint is equivalent to two inequality constraints, the algorithm LTR can be used for solving nonsmooth optimization problems with equality and inequality constraints.

同时，由于等式约束等价于两个不等式约束，故算法LTR也适合于求解带一般线性约束的非光滑优化问题。

Then we derive first-order necessary optimality conditions for optimization problems with affine variational inequality, which joint upper-level feasible region Z includes a linear inequality constraint and a linear equality constraint.

其次，我们研究Luo的带仿射变分不等式约束优化问题，其中上水平约束Z不仅含有线性不等式约束，而且含有等式约束情形时的一阶最优性条件，同时还给出了Z的切线锥的表达式。

For a general system, our Lyapunov function-based method can give a low conservative estimation for the region of attraction, moreover, a much more large region of attraction by using Matlab/LMI optimization.

对一般系统，我们用基于Lyapunov函数的方法给出保守性尽量低的吸引域的估计算法，再配合基于Matlab线性矩阵不等式优化方法去综合控制器，以便得到尽量大的吸引域。

The stability region estimation of the singularly perturbed systems can be replaced by that of the adjoint systems, and an optimization method based on linear matrix inequality was provided to reduce the conservativeness in the estimation.

将原系统稳定域估计问题转化为低阶伴随系统稳定域的估计问题，利用线性矩阵不等式(Linear matrix inequality， LMI)优化方法估计伴随系统的稳定域以减少保守性。

It transforms the primal problem into an ordinary optimization problem with an explicit dual function and simple constraints, with smaller size than primal constraints. It is convenient for engineering application.

该方法不仅给出了原问题显式形式的对偶函数，而且对偶变量的数目仅等于原问题部分约束的个数，原来的线性0-1规划问题被转化为只有简单约束的普通优化问题，极大地方便了工程应用。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。