数学规划

The convex quadratic programming is an important branch of mathematical programming.

凸二次规划是数学规划中的一个重要分支，它在经济，市场均衡，管理，军事等各个领域均有重要应用。

These results can help us to deeply understand the first and second-order expansion of f on the U -space.

UV-分解理论可应用到数学规划中：对于有限个约束的非线性规划问题，可以对这一问题所对应的精确罚函数作UV-空间分解。

The mathematical programming formulation and related solution procedure are established by the traditional BEM. Through the discretization of space and time, the elastoplastic stress simulation method and reduce-basis technique are adopted to construct the self-equilibrium stress field. The numbers of variables and constraint equations in the resulting mathematical programming formulation are reduced greatly and then the dimension obstacle of computation in 3-D limit and shakedown analysis is overcome.

采用常规边界元方法建立了三维结构极限与安定分析的数学规划格式，通过对时间和空间的离散化，并采用弹塑性模拟法构造自平衡应力场和引入减缩基技术，大大减少了所形成的数学规划格式中的未知变量和约束方程的数目，有效地克服了三维结构极限与安定分析中的维数障碍问题。

The first part of the paper focuses on Saddlepoint Programming . It explicates SP's origin background, classification and relationship with other mathematical programing . The optimal conditions of SP has been proven and its geometric interpretation has been made.

文中首先讨论鞍点规划原理，阐明了这种规划产生的工程背景、分类、数学表述及其与一般数学规划的关系；证明了鞍点规划最优性条件的有关定理，并给出了几何解释。

The optimal design of layout programming of RRMS is explored. The mathematical programming model based on matroid is established and the greedy method is selected serving as the optimal method. The application program based on this method is also developed and compiled.

摘 要：研究探索了快速可重组制造系统布局规划中的优化设计问题，建立了基于拟阵的数学规划模型，通过对比选取贪馋算法作为优化算法，并编制开发了此算法的应用程序。

Quadratic programming is a special form of mathematicalprogramming,and has close connect...

二次规划作为一种特殊类型的数学规划，与许多力学问题有着密切联系。

Quadratic programming is a special form of mathematicalprogramming,and has close connection to many problems in mecha-nics.

二次规划作为一种特殊类型的数学规划，与许多力学问题有着密切联系。

On this basis, according to historical data, apply ANN and differential simulation method to get the quantitatively correlative relations between each production and its own influence factors, and introduce the new methods of prediction for dynamic indexes with gas-field development (The combinatorial prediction method based on fuzzy comprehensive evaluation, the method of ANN to select optimally combinatorial prediction models and the ANN prediction method based on genetic algorithm).(2) Base on mathematical programming, combine with quantitative economics and techno-economics, introduce economical indexes to establish production"s distribution optimal model, production"s constitution optimal model and measured production"s constitution optimal model, including multi-objective models and five-years models. Upon this, the optimal project for all gas field and each gas-collected factory can be got. Also, introduce the time value of capitals to improve on these models.(3) Base on the optimal solution theory and algorithm theory for the nonlinear programming problem, introduce the SUMT algorithm and genetic algorithm to study how to solve the models, and on the basis of normal genetic algorithm, make use of auto-adaptively modulating method to improve on normal genetic algorithm; Base on algorithm"s convergence theory and calculation"s complexity theory to analyze seriatim SUMT algorithm"s convergence and genetic algorithms convergence, and compare performance with each other.

在此基础上，利用神经网络方法和微分模拟方法根据历史数据得到各分项产量与其影响因素之间的定量关联关系，并引入气田开发动态指标新的预测方法(基于模糊综合评判的组合预测方法、神经网络优选组合预测模型预测方法以及基于遗传优化的神经网络预测方法)；(2)以数学规划为基础，结合数量经济学和技术经济学，引入经济指标建立产量分配优化模型、产量构成优化模型、措施产量构成优化模型、气田开发多目标规划模型以及五年规划模型，进而获得全气田及各采气厂的最优方案，并引入资金时间价值对五年规划模型进行改进；(3)以非线性规划问题的最优解及算法理论为基础，引入SUMT算法以及遗传算法对模型的求解进行研究，并在原有的遗传算法基础上，引入自适应调整方法对遗传算法进行改进；以算法的收敛性理论和计算复杂性理论为基础，逐一分析SUMT算法以及遗传算法的收敛性，并比较三种算法的优劣性。

The stochastic programming becomes a common programming after the expectation is gotten. An algorithm is given to solve this kind of programming.

在求得模型中各随机变量的数学期望之后，将随机规划问题转化为通常的数学规划问题，并给出了求解这类问题的一个算法。

In chapter three, with the effective combination of the prior preference, posterior preference and interactive method, and based on the theory of satisficing decision making and goal programming, an interactive method for solving static or dynamic multicriteria programming is devised. In the method, by constructing the simplexes in the set of parameters and transforming them, the local preference information is interactively quested in th process of decision making. The prior and posterior preference are used to speed up the process of decision making and overcome the false convergency which may be occured in pure interactive algorithms. This method can be used to cope with linear, nonlinear and dynamic multicritcria programming.

在第3章多目标数学规划的参数单纯形方法中，通过多目标数学规划的验先偏好方法，交互式方式与验后偏好方法的有效组合，在满意决策和目标规划的理论基础上提出了一种求解多目标静态及动态规划的交互式方法，该方法通过在参数集中构造单纯形并进行其变换，在决策过程中交互地索取决策者的局部偏好信息，并利用决策者的验先偏好来提高决策过程进行的速度，及利用决策者的验后偏好来克服纯交互式算法中可能出现的假收敛现象。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。