有效函数

Conjugate direction algorithm is an important algorithm in the theory of optimization.

引言 在二次函数的最优化算法中，共轭方向算法是一种最有效的方法。

As to the remaining parameters, two methods are developed: first, accepting that the projection function complies with a circular function within at least a part of a given field of view, constrained by the obtained object-to-image radial mapping and a constant focal length, the best-fitting point of the optical origin is tested along the optical axis; secondly, referring to the postulation of the exclusively bilateral mapping between an imaged point and its scenic sight ray, a measuring technique is developed to survey the world coordinates which will fabricate a projecting path to the imaged points located on the imageable region of the image plane in order to directly model the projection geometries involved.

而针对其余参数本文提出两种解题方法：其一是根据『在「部分视野角范围」内，鱼眼相机的投射模型符合一典型的「圆形函数」』以标靶实体与其影像尺寸为限制条件，测试光学轴上的最佳视觉参考点、鉴定最适当的投射模型、焦距、及有效的视野角度范围。其二是根据『一视野线排他性地与对应「呈影点」一一映射』参考一呈影点来搜寻空间中对应视野线的绝对座标后，据以演绎相机内部影像形成的模型。

The user's utility is a function of his data throughput, thus the bandwidth resource utilization problem is modeled as a utility based constrained maximization problem, called a system problem.

通过设置站点吞吐量的对数效用函数，将带宽资源的有效利用问题建模为系统效用最大化问题；应用最优化理论将此系统问题等效为可分布式求解的用户问题，即各站点只须独立选择最大化其净效用的竞争参数，则系统整体效用也获得最大化。

The continued fraction approximation is developed in reliability analysis for slope stability, the features of this method are rapid speed of calculation, simple and direct, high precision and effectively combin ing method of fixed value with probabilistic method on stability analysis for slope.

在斜坡的可靠性分析中，引入了函数连分式渐近法，其特点是计算速度快、简捷、精度高，有效地将斜坡稳定性评价的定值方法和概率方法有机地相结合。

Simulat ion shows that the improved neural network has successfully modeled the continuo us flow stirred tank reactor system.

该算法提高了径向基函数神经网络的泛化能力和鲁棒性，研究表明是一种有效的"黑箱"动态建模方法。

By applying contour integral method and high-order displacement functionsof MM,we obtain the accurate stress intensity factors of mixed-mode crack.Then,the open crack propagation of the mixed mode I and II is simulated by means oftheories of linear elastic fracture mechanics.This provides a simple and effectivenumerical way for crack evolvement studying.

接着，文中采用围线积分法和流形方法的高阶位移函数来计算得到比较准确的混合型裂纹尖端的应力强度因子，然后基于线弹性断裂力学的裂纹扩展准则，用流形方法实现了平面I-II混合型张裂纹扩展的数值模拟，为数值方法研究裂纹的演化行为提供了一条简单而有效的途径。

And its convergence property, asymptotically converges in probability, is proved. Numerical results on some typical optimization problems show that the algorithm proposed is efficient.

数值结果表明，对于维数较高的连续函数优化问题，采用基于均匀分布的进化策略能够快速有效地收敛到全局极小点。

The experimental results using the testing functions show that CPSO is able to search the global optimizer and avoiding the premature convergence on the multidimensional variable space.

几种典型函数的测试结果表明：CPSO提高了对多维空间的全局搜索能力，并可以有效避免早熟现象。

Secondly, it analyses and designs the network model and its nature by means of convex quadratic function.

摘 要：从给出供应链的费用结构和消费结构出发，在产销平衡和市场平衡的条件下，考虑制造商、销售商和消费者等多种因素，建立一类供应链平衡网络模型，并借助凸二次函数的性质研究这类问题的模型和性质，进行定量分析，设计有效的求解算法。

Variable and fixed cost behavior patterns are valid for linear cost functions only within the given relevant range.

在线性成本函数中，只有在给定的攸关范围内，变动及固定成本的习性类型才是有效的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。