约束优化

In Chapter 5, a new method with direct partitioned column updates of cholesky factorization for solving large scale sparse unconstrained optimization problems is proposed, which depends on a consistent partition of the columns and cholesky factorization of the Hessian matrix.

第5章基于稀疏Hesse阵的列的相容分划，并在其Cholesky分解的基础上建立了求解大型稀疏无约束优化问题的直接校正Cholesky因子算法。

For the ill conditioned load flow caused by the error produced in the transformation from electricity quantities to average power, direct current load flow and sensitivity vector are presented to find out the ill node, then by adjusting the load curve and generation curve in a certain principle, which is shown in detail with several flow charts, a new operation mode is reestablished to ensure the convergence of the calculation. Optimal multiplier method is proposed to work out the least square solution according to ill conditioned structural power network. The electricity quantities flow method enhances the reliability and accuracy of the calculation of the power transmission losses.

该方法可根据当前输电网中各个变电站24小时的电量记录，利用电量潮流计算对输电网总线损和各条线路损耗进行计算，使计算的精度满足降损措施分析和指标考核的要求；并且对于由负荷出力曲线转化成平均功率计算潮流时引入的误差，进而导致潮流计算不收敛的情况，采用直流潮流法，依据相角对有功功率的灵敏度向量判断出"网络异常点"，并且给出了解决此种情况的方法流程图；针对结构病态的电力系统潮流计算不收敛的情况，运用非线性约束优化方法中的最优乘子法求解潮流方程的最小二乘解，从而解决了电量潮流法计算理论线损时的收敛性问题，增强了该方法的适用性。

For its two special cases: N = 0 and R=0, based on nongradient and gradient methods respectively, neural networks for the two cases are constructed. With the Lyapunov theorem and the LaSalle invariant set principle, the proposed networks are proved to be

推广了R_0性质的定义，并证明无约束优化问题目标函数的水平集的有界性与矩阵对的R_0性质是等价的，最后运用Lyapunov稳定性理论和LaSalle不变原理，严格分析了网络模型的稳定性和收敛性，这些模

In this paper, we start with a new formulation which is proposed based on the K-SVCR method. We then transform it as a complementarity problem and further a strongly convex unconstrained optimization problem by using the implicit Lagrangian function.

在本文中，我们首先在K-SVCR方法的基础上提出了新的模型，然后把新模型转化成一个互补问题，并利用Lagrangian隐函数进一步转化成一个强凸的无约束优化问题。

It is well-known that reduced Hessian method is one of the most efficient methods for solving large scale constrained optimization problems. However, the convergence analysis for the method requires of the positive definiteness of the reduced Hessian of Lagrangian function.

众所周知，既约Hessian方法是求解较大规模约束优化问题的一类有效方法，但已有的这类方法的全局收敛性分析需假定拉格朗日函数的既约Hessian矩阵的一致正定性。

Its global convergence and linear convergence rate were proved under some mild conditions.

提出一类新的求解无约束优化问题的记忆梯度法，在较弱条件下证明了算法具有全局收敛性和线性收敛速率。

In Chapter 4, using the formula A_k(2) given by Wei, we propose a new A_k(2)-SQP method, which develepments the using of the quasi-Newton formula BFGS, and combines with SQP method to solve constrained optimization problems, the corresponding algorithm possesses global convergence and supei linear convergence property.

第四章，利用韦提出的A_κ(2)公式，我们给出了一种A_κ(2)-SQP方法，该方法把拟牛顿修正公式BFGS进行了推广，并结合SQP方法去解约束优化问题，相应的算法具有全局收敛性和超线性收敛性。

A trust region algorithm for special linear inequality constrained optimization problems is proposed in chapter two.

第二章对一类特殊的线性不等式约束优化问题提出了一种修正的信赖域算法。

Reissner topic,which thinks fracture plane behind retaining wall is made up of a logarithmic spiral and a straight line,and by using limit equilibrium and constrained optimization,the formulas of active earth pressure,the resultant force of earth pressure and its application point are obtained.

基于普朗德尔-瑞斯纳课题认为，挡土墙土体破裂面是由对数螺线与直线组成的复合滑动面的结论，采用极限平衡法和约束优化相结合的方法，重新推导了主动土压力及其合力和作用点高度的计算公式。

Parts of current parallel databases support expanding of data types, but all of them lack of theoretical foundation. It is difficult to predicate the performances of parallel query, complicated to optimize parallel query and unattainable to keep the correctness of parallel query optimization This thesis, for the first time, combines monoid algebra system with BSP parallel model systematically, and provides a general-purpose parallel object-relational database systems-PORDBMS.

文章系统地研究了资源分配问题的分解协调理论与方法，给出了非线性分解式模型的构造和有效的求解方法，其中对主问题提出了适应性较强的修正算法，可用于一些难于公式化的问题的模型构造与求解，逐步寻优策略可有效地求解非线性关联约束优化问题。

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。