凸规划

The method of convex quadratic programming relaxation has been used for the scheduling with rejection .

用凸二次规划松弛方法研究工件具有就绪时间，目标函数为工件总拒绝费用与接受工件的带权总完工时间之和的工件可拒绝排序问题，得到界为2的多项式时间近似算法。

Inequality constrained least-square problems are first changed to convex quadratic programming problems and then solved for the optimal solutions.

研究了不等式约束下的平差问题，即先将不等式约束的最小二乘问题转换成凸二次规划问题，然后求其最优解。

When the Hessian is positive definite, the QP subproblem is a strictly convex quadratic programming.

若QP子问题的Hessian阵正定，则它是一个严格凸二次规划问题。

A parametric optimization method for tracking optimal solution's trajectory of linearly constrained convex separable programming was presented.

提出一种追踪线性约束下凸可分规划问题最优解轨迹的参数化方法。

Using the convex set model to describe the uncertainty existed in the parts design.By adopting the physical planning method to construct discontentedness function of the uncertainty parameters.

用凸集模型描述零件设计中存在的不确定性，采用物理规划方法构造不确定性参数的不满意度函数，通过极小化不满意度函数最差值实现目标函数的稳健性，通过灵敏度分析实现约束函数的稳健性。

However, because its feasible region is neither convex nor connected, this problem is intractable. Therefore, the nonlinear programming theory cannot be applied here directly.

然而该问题又是难解的，原因在于它的可行域既不是凸的又不是连通的，所以不能直接用现有的非线性规划理论来解决。

For a class of generalized fractional programming whose objective function is composed of infinite fractions,the saddle-point type optimality criteria are proven by using the existing necessary conditions,under the assumption of the class of B--invexity.

对于一类目标函数中有无限个分式的广义分式规划，给出一个不完全Lagrange函数，并利用已有的最优性必要条件，在B--不变凸性的条件下，证明了鞍点最优性准则。

When initial point is an interior point in the box, the global convergence of the method is proved.

带箱约束的非凸非线性规划有许多不同的应用，但由于它的计算复杂性，一般来说求解十分困难。

Chapter2, mainly summarizing the optimality conditions for the nonconvex semidefinite programming, first recalls the concept of transversality condition, proves that transversality condition and linear independence condition are equivalent, and shows that under strict complementarity condition, the transversality condition is a sufficient condition for uniqueness of the Lagrange multipliers.

第2章，主要综述非凸半定规划的最优性条件，首先回顾了横截性条件的概念，证明了横截性条件与线性无关条件是等价的。并且说明了在严格互补松弛条件下，横截性条件是Lagrange乘子矩阵唯一的充要条件。

Numerical results show that when the parameter is small enough a global minimum point can be always found with this method.

它的特殊情况是带箱约束的非凸二次规划，对这一情况已经提出了几种逼近方法[5，6] 。

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。