数学规划

Based on the convex analysis and duality theorem, a kinematic shakedown formulation for 3-D problems is derived.

根据下限定理，通过引入P泛数，并采用应力函数法构造平衡应力场，建立了极限下限分析的有限元数学规划格式。

Therefore, the research on convexity and generalized convexity is one of the most important aspects in mathematical programming.

因此，对凸函数和广义凸函数的研究是数学规划中最重要的内容之一。

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

We will utilize tabu search and simulated annealing to determine the discrete decisions. Then, by using the discrete decisions, a mathematical programming model, proposed herein, will be used to solve the continuous decisions.

求解方法为先利用塔布搜寻法或模拟退火法找出离散决策，再带入一个以最小化总存货成本为目标的数学规划模式，以求解出连续决策的值与目标函数值。

A DRAT (Dimension Reduction and Absolute value Transformation) Method is proposed, which through the establishment of a minimum set of thelinear parameters in the spectrum model and its absolute value transformation, makes the 3M+1 dimension constrained optimizingprohlem into an equal 2M dimension unconstrained one.

谱峰分离的拟合方法涉及到比较复杂的高维和强非线性的数学规划问题。这使得一些流行的计算方法的收敛性强烈地依赖于初始参数值的质量l'I5l。

The equivalent relation between quasi-semi-E-convexity of functions and corresponding level sets is proved.

函数的凸性与广义凸性在数学规划以及最优化理论中起着非常重要的作用。

We used the modeling tool: Evolver with underlining genetic algorithm to solve the problem and analyzed the modeling results.

本研究设定单期及多期两种生产期间，分别建构完全接单后生产、推迟生产、混合预测性生产与推迟等三种生产策略之数学规划模式，采用基因演算法求解，分别比较演算结果并进行分析。

In the case of the location selection problem, mathematical programming has usually been untilized to determine the optimal location of facilities

在选址问题的情况下，数学规划通常也被untilized确定设施的最佳位置

Mathematical programming is one of the areas to which fuzzy set theory has been applied extensively.

数学规划是模糊集理论应用极其广泛的一个领域。

Preference parameter of decision maker is introduced and generalized compromise solution is proposed for multiple objective decision making problems.

引进决策者偏好参数，提出了多目标决策问题的广义折衷解概念，然后探讨了广义折衷解的性质，最后也给出其数学规划的求解方法。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷