凸规划

Mond - Weir type dual and Wolfe type dual for any dimension programming with equality and in inequality constrains is discussed.

在Banach空间中定义了ρ－不变凸的概念，讨论了具等式和不等式约束的任意维规划的Mond－Weir型对偶与Wolfe型对偶。

By combining analysis center cutting plane methods which have developed fast in the last years, we get a analysis center cutting plane methods for convex semi-infinite programming, which has a good convergence under modest assumptions.

第二章结合近期发展起来的分析中央割平面算法，在一定的假设条件下，得到了一个凸半无限规划问题的分析中央割平面算法，并得到了很好的收敛性结果。

Based on the relationship between matrix and symmetric matrix global exponential stability of the discrete-time neural networks model and the result of exponential convergence rate were obtained by using the characteristics of eigenvalues of a positive definite matrix and introducing a proper factor.

针对带有边界约束的凸二次规划问题，利用离散神经网络模型的建模原理，构造了一个神经网络模型。利用矩阵与对称矩阵的关系和正定矩阵特征值的性质，通过引入一个适当的因子，得到了该离散型神经网络模型是全局指数稳定性和指数收敛率的结果。同时分析了该结果的优越性和存在的不足，提出了解决的3种方法，最后给出了实例说明本方法取得结果的实用性

However, the higher computation costs of quadratic optimization problems of the algorithm limit its applications on large data sets.

然而，该算法的凸二次规划问题优化求解的较高的计算复杂度限制了其在较大规模数据集上的应用。

The new approach improves the step length and the convergence is analyzed. Numerical examples are given to illustrate the effectiveness of the proposed method.

在此基础上提出了求解只带有等式约束的凸二次规划问题的新算法，该算法改进了搜索步长，分析了收敛性，通过数值算例验证了算法的有效性和优越性。

Meanwhile, we have gotten stability for the subdifferential of cone efficient point sets and cone weakly efficient point sets of multiobjective programming with respect to perturbation of cone respectively.

对于局部凸拓扑向量空间的多目标规划问题，本文研究并得到当确定空间序的控制锥受扰动，它们的锥有效点集和锥弱有效点集分别在锥次微分和锥弱次微分意义下的稳定性结果。

In the sense of weak effective solution,the problems of Lagrange duality and saddle point are discussed under the convexlike condition.An alternative theorem of the system containing a semidefinite constraint of a matrix function is established at first.

首先在似凸条件下建立了一个含矩阵函数半定约束系统的择一性定理，由此得到多目标半定规划及其在弱有效解意义下的Lagrange对偶理论，包括弱对偶、强对偶和逆对偶等。

Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.

将线段长度与线段之间的角度作为表示参数，既有利于能量函数的构造，又便于处理位移约束和长度内蕴约束条件，利用这一优势，将其应用于三维人体的参数化建模，可以方便地产生具有不同特征尺寸参数的人体模型，由于这种方法只适用于折线变形，具有较大局限性，因此，本文进一步提出一种较通用的离散曲线曲面变形方法，通过分析变形前后的位置关系来构造能量函数，再加上位移约束条件，将变形问题转化为一个凸二次规划问题，并且给出了约束点应满足的必要条件及模型解唯一的充分条件，这种方法还可以与骨架驱动变形的思想相结合，能更好的控制变形。

The topics covered in this course include: unconstrained optimization methods, constrained optimization methods, convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming.

这门课程的主题包括：无约束最优化方法，约束最优化方法，凸分析，拉格朗日松弛法，不可微函数最优化，以及在整数规划上的应用。

The topics covered in this course include: unconstrained optimization methods, constrained optimization methods, convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming.

这门课程的主题包括：无限制最适化方法，限制最适化方法，凸分析，拉格朗日松弛法，不可微分函数最适化，以及在整数规划上的应用。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。