| 1. | Duality in optimization involving a type of invexity
一类不变凸最优化问题的对偶理论 |
| 2. | Many algebraists are engaged in studying this theory
许多代数学家均从事morita对偶理论的研究。 |
| 3. | Contrastive analysis of the economic interpretation two different kinds of duality theories
两种不同对偶理论的经济意义对比分析 |
| 4. | Since then , the theory of morita duality has become one of the important fields of ring theory and module theory
Morita对偶理论起源于数域上的向量空间的对偶空间理论。 |
| 5. | There is also a comprehensive treatment of optimality conditions , lagrange multiplier theory , and duality theory
这门课程也包括了对最适化条件，拉格朗日乘数理论，和对偶理论的综合论述。 |
| 6. | 2 . a new structural optimization algorithm combined with the half - determined ga and the hybrid approximation techniques is proposed
利用混合近似技术和对偶理论，建立了一般的基于遗传算法的结构优化设计的框架。 |
| 7. | We first transform the vqbp into another value - type bilevel programming problem , in which there is only one unconstrained quadratic sub - program in the lower - level
首先利用数学规划的对偶理论，将所求双层规划转化为一个下层只有一个无约束凸二次子规划的双层规划问题。 |
| 8. | Firstly , the duality principle is used to change the linear program problem into the minimax problem , an interval extension of the adjustable entropy function is set up and its order of convergence is discussed
首先利用对偶理论将线性规划问题转化为极大极小问题，建立并讨论了调节熵函数的区间扩张及其收敛阶。 |
| 9. | In the late 60 ' s integrated theory came up , one of its ways was based on conjugate function theory introduced by fenchel , which rochafellar had developed and improved in a series of his books
六十年代后期，凸规划更完全的对偶理论出现了，其中一种方式是基于fenchel引进的共轭函数概念，这些后来在rockafellar的一系列著作中得以发展完善。 |
| 10. | 4 ) an algorithm for reliability upper bound assessment of large - size network is presented , which is based on the principle of topological classification of node - set ; and the lower bound can be also obtained by dual graph of oriented network .
应用图论的点集拓扑分类原理，提出一个计算大型复杂网络可靠度上界的类分法，并应用对偶理论求解网络可靠度的下界。 |
