| 1. | A quasi - newton method on convex optimization
求解凸规划问题的一种拟牛顿算法 |
| 2. | The affine scaling algorithm for convex programming with linear constraints
线性约束凸规划问题的仿尺度算法 |
| 3. | Convex programming problem
凸规划问题 |
| 4. | In [ 6 ] , rockafellar had deduced the fenchel theory , but some nonlinear programming could not get the dual by fenchel theory directly and dual theory could not be applied in solving some problem
在文[ 6 ]中， rockafellar导出了fenchel对偶定理，然而有许多凸规划问题直接使用fenchel对偶定理很难用显式表示其对偶，有的问题甚至不能直接使用fenchel对偶定理。 |
| 5. | The generalized support vector machines ( gsvms ) was proposed by mangasarian , but it can not be degenerated to the standard svms . in fact , the former only consider the strict convex programming , while the latter considers the convex programming
Mangasarian提出广义支持向量机，但不包含标准的支持向量机：前者研究一般的严格凸规划问题，而后者针对的是特定的凸规划问题。 |
| 6. | The module conversion for a kind of max - min problems is given , namely , the max - min problem with equality and inequality constraint is converted into convex problem with linear constraint , which provides theoretical basis for designing effective algorithms
最后，给出一类极大极小问题的模型转化，把带等式、不等式约束的极大极小问题转化为带线性约束的凸规划问题，这为设计更为有效的算法提供了理论依据。 |
| 7. | The paper discusses convex programs with an additional reverse convex constraint and gives the properties of the global optimization about this problem . a branch - and - bound algorithm for solving this problem is constructed and the convergence properties of this algorithm is analysed
讨论带一个反凸约束的凸规划问题.给出了整体最优解的特性，利用此特性借助分枝定界方法，构造出求该问题整体最优解的算法，并进行了收敛性分析 |
| 8. | According to the dual theory , a simple geometric programming was proposed to derive a corresponding geometric dual problem instead of cross - entropy optimization problem with cross - entropy constrains , which is a concave programming one with linear constrains , leading to a simpler calculation
根据对偶理论，提出了一个简单的几何规划，该方法把一个带有叉熵约束的叉熵优化问题转化成了一个对偶规划，而对偶规划是一个只需要解决一个带有线性约束的凸规划问题，比较容易计算。 |
| 9. | It is significantly important to discuss semidefmite programming . its most important applications are found within many fields ; on the other hand , several classical optimization problems can be formulated as standard semidefinite programming . therefore semidefinite programming provides a unit form to study these problems and construct algorithms
半定规划为研究这一系列凸规划问题并构造算法提供了统一的数学框架，而且半定规划在控制理论、信号处理、特征值优化和组合优化等领域已获得成功的应用，因此半定规划在近几年备受关注。 |
