约束最小化

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。

Where .We assume that f is continuously differentiable, but that information about

为了简单，我们在文中将注意力集中在无约束最小化问题上

Sensitivity function and control sensitivity function are obtained by Youla parameterization of controller,which is used to describe an integral square performance criterion containing tracking error and control energy.

由控制器Youla参数化得到控制系统的敏感度函数和控制敏感度函数用来表示一个包含跟踪误差和控制能量在内的积分平方性能指标，针对不同类型的时滞过程运用谱分解的方法最小化该性能指标，从而导出相应控制器的设计方法，可使系统在控制能量约束条件下具有最优的控制性能。

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。

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。

The features include:(1) objective, which is maximum of economic and noneconomic benefit minimum of economic and non-economic risk;(2) limited reason, which is caused by the uncertainty of environment, bias and incompletion of information and limited ability of information treatment or unreasonable behave of individual;(3) asocial, which is maximum of self-benefit of individual and object conflict between individual and organization.

这些特征包括：(1)决策目标：经济与非经济利益的最大化，经济与非经济风险或损失最小化；(2)有限理性：存在环境的不确定性、信息的不完备和不对称，有限的信息处理能力或说个体行为的非理性化；(3)投机性：存在个体的追求自身最大利益的行为、个人或组织之间目标的冲突、约束制度的不完善等。

First, we have proved that the constraint of local constant gradient angles is equivalent to the minimization of total variation. Based on this, a stronger continuity constraint of gradient angle is presented. The interpolation formula (a 3-degree-PDE) derived from the constraint can ensure the continuity of level lines and reduce the width of edges. The contrast invariant of the regularizer of the formula is also proved.

首先证明了局部恒定的梯度角约束插值等价于总变分最小化；在此基础上，提出一个具有更强连续性的梯度角约束，由这个约束条件导出的三阶偏微分方程使插值的图像既可以保证水平线方向的连续性，又减小图像边缘的宽度；最后证明了插值方程中正则项的对比不变性。

After that, the process and method of life-cycle design are studied according to the process of green product life-cycle and the priority strategies of life-cycle design are concluded as a whole. In chapter 4, argues that Clean Production Technology conciliates social economy development and environment protection on the basis of relationship analysis among society economy, environment and clean production technology from the perspective of modern Eco-economics. It is proposed that resources cost should be equal to marginal opportunity cost from the point of sustainable development.

第四章从现代环境经济学和可持续发展观点出发，深入地分析了社会经济、环境和清洁化生产技术之间的关系，并从可持续发展角度出发阐释了以边际机会成本作为资源成本的原由及构成；在此基础上，采用数学方法分析了企业清洁化生产的过程，推导了企业清洁化生产资源边际机会成本最小化的约束条件，并研究了企业清洁化生产的技术、经济、环境数学模型。

Based on the minimum cross entropy theory ,a new model,which can forecast mortality distribution by minimizing the cross entropy function subject to the future life expectancy of insurants,is proposed.

基于最小叉熵原理，建立了预测被保人死亡率分布的一个模型——最小叉熵模型，该模型以叉熵函数作为目标函数，以被保人的预期寿命作为约束条件，通过最小化叉熵预测被保人的死亡率。

The method of minimizing the Expected Shortfall: the Pflug-Rockafellar-Uryasev method was introduced and was extended to HARA Spectral Measure of Risk M_. Constrained risk-reward optimization is in factshown to coincide with unconstrained minimization of particular spectral measures.

介绍了α-ES最小化的Pflug-Rockafellar-Uryasev方法将其推广至双曲类风险厌恶函数谱测度M_φ约束下的优化问题，证明了经典的马科维茨风险收益问题与对应的无条件限制的谱度量最小化是一致的。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。