凸规划

With the Ben Tal generalized algebraic operation of 2 , we obtained some necessary and sufficient conditions for the class of generalized convex programming, and the results generalize the corresponding ones for the convex Programming.

利用文〔2〕中定义的Ben－Tal广义代数运算，本文得到了这类广义凸规划的Kuhn－Tucker充分条件和必要条件，所得结果推广了通常凸规划相应的结

In this paper, based on the conjugate function and the dual programming of convex programming, with the dual cone, to conic programming, the dual programming is fully discussed, the expression of the dual programming is educed, the main dualities are proved, and the dualities of the familiar conic programming are studied.

以共轭函数和凸规划的对偶规划为基础，利用对偶锥的概念，全面讨论了一般锥规划的对偶问题，严格推导出锥规划对偶规划的表示形式，给出了锥规划的主要对偶性质，并用这些结果研究了常见锥规划的对偶性。

There are a lot of conclusions about properties of convex set and convex function, which have full application in convex programming.

相应于凸规划的凸集和凸函数的性质已有很多结论，并且在凸规划的研究中得到了充分应用。

This paper is a discussion of new algorithm for convex objective function and convex programming with constraints.The algorithm is an extension and improvement for a new linear programming.

对一般凸目标函数和一般凸集约束的凸规划问题新解法进行探讨，它是线性规划一种新算法的扩展和改进。

We also construct an algorithm for minimizing its Moreau-Yosida regularization, because this is a smooth convex optimization problem.

极小化一个凸函数可以采用在UV-空间分解理论基础上提出的概念型超线性收敛算法，也可以采用极小化这一凸函数的Moreau-Yosida正则化函数的算法，因为这是一个凸规划的光滑最优化问题。

And a counter example about a result of E-convex programming is given.

给出了一类广义的凸集和凸函数——E-凸集和E-凸函数的一个性质；并给出了关于E-凸规划命题的一个反例。

And this paper built a simulation model of distribution system with discrete requirement through computer simulation software.

通过计算机仿真，文章对离散需求的分销系统进行了模拟，并将结果与凸规划模型进行了比较，结果证明，凸规划模型在离散需求情况下也是基本适用的。

Markowitz model of equality constraint protrusion analysis is constructed,including the generic restriction conditions.

文章在将一般化的约束条件纳入分析框架的基础上，建立起Markowitz等式约束凸规划分析模型，运用二次规划问题降维算法的原理，提出了一个求解Markowitz等式约束凸规划模型的快速算法。

In first part it pays attention to theory study. Afterwards, based on linear programming, we introduce some properties of conic optimization and its dual problem, which are a kind of especial convex programming. In second part, we apply these theories to practice, such as least-squares problems, polynomial solution and approximating covariance matrices, and other aspects .

第一部分是理论研究：在线性规划的基础上重点介绍了一种特殊的凸规划类型——锥规划及其对偶锥规划，并介绍了锥规划及其对偶锥规划的发展及其性质。

Semidefinite programming is a subfield of convex optimization where the underlying variables are semidefinite matrices .

凸规划研究的情况下，目标函数是凸的限制，如果有的话，形成一个凸集。

Objective: To study the effect of polycythemia on blood oxygen saturation.

裴蕾目的：观察RBC剧增而引起的高粘血症对血氧饱和度的影响。

Based on SIMPLER algorithm in the curvilinear body-fitted coordinates, the calculations were performed for Pr=0.7, Re=10~1000 on non-orthogonal non-staggered grids which are generated by elliptic equation systems.

采用曲线坐标系下压力与速度耦合的SIMPLER算法，数值研究了周期性渐扩渐缩波纹通道内脉动流动与换热情况，流动Re数的范围为10~1000，Pr数为0.7。