最小化

We introduce the basic concepts needed to analyze the estimation error in VC theory by showing the connection between Empirical Risk Minimization consistency and uniform convergence and illustrate necessary and sufficient conditions for the consistency of the ERM principle, that is for the convergence of the minimum of the empirical risk to the minimum of the expected risk.

为了整合最小化经验风险和最小化期望风险理论，我们将藉由最小化经验风险(Empirical Risk Minimization， ERM)及统一收敛性举例说明原理的必要与充份条件，以分析VC计算理论的误差估算所需的基本概念。

Firstly, the approach formulates a cost functional to turn the inverse problem into a constrained minimization problem according to least squares criterion, then the resulting constrained minimization problem is transformed into an unconstrained minimization problem by using a penalty function technique, and then the closed Fr chet derivatives of the Lagrange function with respect to the properties are derived based on the calculus of variations, finally, one can solve the resulting problem by using any gradient-based algorithm and the finite-difference time-domain method.

该方法首先以最小二乘准则构造目标函数，将逆问题表示为约束最小化问题；接着应用罚函数法转化为无约束最小化问题；然后基于变分计算导出闭式的拉格朗日函数关于特征参数的Fr chet导数；最后借助梯度算法和时域有限差分法迭代反演德拜模型参数。

For example, Gilbert et al.(1985) developed a model that optimizes the selection and layout of a set of connected cells, such that the cost of purchase and development is minimized, the distance to 'detractor' cells is maximized, the distance to 'amenity' cells is minimized, and the 'diameter' of the layout is minimized.

比如说，Gilbert 等人建立了一个使一系列相连单元的布局最优化的模型，因而购置所需的费用被最小化，距离"谤者"单元的距离最大化，到"舒适"单元的距离最小化，布局的直径最小化。

Firstly, applying spectral factorization to minimize an integral square performance criterion containing tracking error and control energy, an optimal control law for the nominal model is derived on condition of control energy constraint. Then, for model uncertainty, using spectral factorization to minimize the variance of the actual system performance from the nominal performance over all frequency range, a robust controller design method is abtained, which has optimal robustness of the system nominal performance to model errors.

首先针对控制对象的标称模型应用谱分解最小化一个包含跟踪误差和控制能量在内的积分平方性能指标，导出一个控制能量约束条件下的最优控制律；然后再针对模型不确定性应用谱分解最小化实际系统性能和标称性能在整个频段上的方差，得到一个鲁棒控制器的设计方法，可使系统的标称性能对模型误差具有最优的鲁棒性。

On the design of algorithms, a novel exact hierarchical delay analysis method for general circuits is proposed; based on the sensitization theorem for sequential circuits, an exact minimizing clocking method is proposed; based on Boolean process, a waveform simulation method considering interconnecting delay for logic circuit and a parallel waveform simulation method are proposed; a new method that transforms bit-level waveform polynomial to word-level polynomial model is proposed; a multiple valued synthesis algorithm based on multiple valued Boolean process and a wire-centered delay synthesis policy are proposed, in which timing planning, floorplanning, wire planning and optimal clock skew in early design are considered; a two-layers channel routing method for minimizing crosstalk under grid mode is proposed; based on the transition numbers theorems for waveform polynomial, a new method for generation of test with noise effects is proposed.

算法设计方面，提出了一种精确的通用电路层次化延时分析方法；基于时序电路的敏化定理提出时序电路最小时钟周期精确确定方法；提出基于Boolean过程论的考虑互连延迟的逻辑电路波形模拟方法，在分析了波形模拟适合并行化基础上，进一步提出一种并行波形模拟算法；提出一种将位级电路波形多项式描述转化成字级多项式描述的新方法；提出一种基于多值Boolean过程的多值电路综合算法以及一种将前期设计定时规划、前期设计的布局规划和线网结构化方法及低偏移的时钟分配等技术相结合的面向互连延时的综合策略；提出一种串绕最小化的网格模式下的双层通道布线方法；从波形多项式描述跳变数的定理出发提出了一种考虑噪声效应的测试生成新方法。

The results of numerical experiments, using the four-dimensional variational data assimilation system of the nonhydrostatic mesoscale model MM5, show that: the tangent linear model and adjoint model conducted by keeping the "on-off" switches the same as the basic state, can provide a good approximation of the first-order information to the NLM perturbation and a good descent direction for the minimization procedure; switching on and off at every other time step in the Kuo cumulus parameterization scheme don"t impact the convergence rate of cost function; the existence of the switches don"t impact improvement to the MM5 model rainfall prediction because that not only specific humidity ,but also wind, temperature and pressure are assimilated into the model.

非静力中尺度数值模式MM5的四维变分资料同化系统进行的数值试验结果表明："开关"变量保持与基态一致，所构造的切向线性模式能够提供关于非线性模式扰动的一阶近似，伴随模式所计算的梯度值能够为最小化过程提供较好的下降方向；郭氏降水参数化方案中对流每隔一个积分步的交替发生并不影响目标函数最小化的收敛速度；"开关"变量的存在也不影响将风、温度、气压和比湿结合起来同化对MM5降水预报准确性的提高。

The paper proposes the TLS approach that minimizes the two kinds of errors.A Rayleigh Quotient formulation based on regularization is used to enforce a smooth solution.Then a conjugate gradient algorithm is used to minimize the modified RQ function.

该方法能同时最小化这两种误差，采用基于正则化的Rayleigh商来光滑解，用共轭梯度算法来迭代求解该正则化Rayleigh商的最小化函数。

The features of the design approach are that the coupling function between water utilization network and heat exchange network is considered;in the first stage,the step-by-step double-linear programming method is employed for the design of water utilization network targeting both minimum water consumption and minimum energy loss,realizing the minimum water consumpt.

其特点是：考虑了用水网络和换热网络之间的耦合作用，在设计的第一阶段即用水网络设计阶段，以同时的用水量最小和火用损最小为目标采用逐步双线性规划法来设计用水网络，实现整个过程的用水最小化并为第二阶段的换热网络设计提供最合理的冷流和热流股以确保能量的合理利用；对于设计的第二阶段的换热网络设计，可直接采用文献中的方法。

At each level, the parameters, hyper parameters and model parameters are adjusted to minimize the Kullback-Leibler divergence between their posteriors and real distributions so that the variable free energy can approach the real free energy.

在指出证据框架和自由能最小化方法等贝叶斯推理方法的局限性的前提下，通过对比证据框架的方法，提出了自由能框架的概念，将通常难以求解的自由能最小化过程分解成参数自由能最小化、超参数自由能最小化、模型参数自由能最小化等层次，在每个层次上调节参数、超参数和模型参数，使其后验分布为其真实分布之同的Kullback-Leibler距最小，以使可变自由能逼近真实自由能。

The aim of the contour optimization is at minimizing and uniforming the tangential electric field as well as minimizing the size of the suspension insulator, subjected to design constraints.

悬垂碍子外型之最佳化设计之主要目的在於满足设计限制式之条件下，将碍子表面之切线电场作均匀化与最小化，并且对碍子绝缘尺寸作最小化设计。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失