极大值问题

As a result, it shows thatthe static or dynamic subsystem optimum alone is not equal to the system optimum. Three initial value problems met in the optimal design of flying vehicle are studied andconclusions are derived that: orthogonal test method can be adopted to decide the initial valueof static optimization problem, some mathematical techniques can be used to deal with thecostate variables of Maximum Principle and decide the initial value of the costate variable,the indirect method can be used to get the analytical solution under ideal case to guide thechoice of the initial control curve in the direct method. With some numerical examples oftrajectory optimization, it shows that all these methods are useful not only in accelerating theconvergence but also in converging to the global optimum.

针对飞行器优化设计中的三种初始值问题进行了研究，以远程弹道导弹弹道的工程优化为例说明，对于静态优化问题，采用正交试验法选取初始值，不仅可以大大加快收敛的速度，而且更有可能收敛到全局最优解；以气动力辅助变轨问题为例说明，用共态变量的一阶泰勒级数展开可以解决极大值原理中共态变量初值难于确定的问题；以二级弹道导弹的主动段弹道优化为例说明，利用间接法在理想情况下得到的解析解来指导直接法初始控制曲线的选择，将大大有利于提高直接法的收敛速度。

Based on the theory of isomorphic mapping and singular value decomposition theorem, the maximum of the kernel Fisher discrimination criterion can be skillfully acquired by solving the minimum of its reciprocal in a small space, and the final solution is acquired without taking account of the null space and non-null space of the kernel within-class scatter matrices separately.

基于同构映射原理和奇异值分解定理，在一个更小的空间内将核Fisher描述准则函数的极大值问题转化为其倒数的极小值问题，使最终的解不需要分开考虑核类内散度矩阵的零空间和非零空间。

Based on Pontryagin maximum principle,the lunar soft landing problem is transformed into a two-point boundary value problem in mathematics.

首先，从庞德里亚金极大值原理出发，将有限推力作用下月球软着陆问题转化为数学上的两点边值问题；在考虑边界条件及横截条件的前提下，将该两点边值问题转化为针对共轭变量初值和末时刻的优化问题；然后应用非线性规划方法求解所形成的参数优化问题。

On this basis, anoptimization algorithm library named OPTLIB is formed. The study of dynamic optimization theory is followed. To solve the problem of thecoupling of the static and the dynamic parameters of the flying vehicle design, some auxiliaryvariables are introduced to deal with them together. Then the calculus of variation is adoptedand augment form of Pontryagin's Maximum Principle is derived.

研究了飞行器设计中的典型动态优化问题——轨迹优化问题及算法，针对飞行器设计中的静态参数和动态参数互相耦合的问题，引入辅助变量将静态参数和动态参数统一处理，在此基础上用变分法推导了极大值原理的增广形式，证明了单独的静态或动态最优并不等于总体最优。

Based on Pontryagin maximum principle, the lunar soft landing problem is transformed into a two-point boundary value problem in mathematics. In consideration of the bound condition and transversality condition, the resulted two-point boundary value problem is converted into a parameter optimization problem aiming at the initial values of conjugate variables and the terminal time, then it is solved by the nonlinear programming.

首先，从庞德里亚金极大值原理出发，将有限推力作用下月球软着陆问题转化为数学上的两点边值问题；在考虑边界条件及横截条件的前提下，将该两点边值问题转化为针对共轭变量初值和末时刻的优化问题；然后应用非线性规划方法求解所形成的参数优化问题。

Firstly the dimensionless planar motion model of SGKW was established;then the optimal control problem of shortest time coplanar hit orbit was transformed into two-point boundary value problem by means of Pontryagin maximum principle .

首先建立了SGKW的无量纲化平面运动模型，然后利用庞特里亚金极大值原理将时间最短共面打击轨道的最优控制问题转化为两点边值问题。

This OCVC problem was converted to a typical two-point boundary-value problem according to Pontryagin maximum value principle, and this TPBVP was a first order optimality condition which could be solved by Radau collocation method.

根据Pontryagin极大值原理建立该协调电压控制问题的1阶最优性条件，该条件是一个典型的两点边值问题。在此基础上采用拉道排列法求解这个两点边值问题。

According to the requirement of a minimum-fuel-consumption, a method of coplanar hit orbit optimization design for SGKW was studied. The dimensionless planar motion model of SGKW was founded, and the optimal control problem of minimum-fuel-consumption coplanar hit orbit was derived into two-point-boundary-value problem according to Pontryagin maximum principle.

针对燃料最省要求，研究了SGKW共面打击轨道优化设计方法，建立了SGKW的无量纲化平面运动模型，利用庞特里亚金极大值原理将燃料最省共面打击轨道的最优控制问题转化为两点边值问题。

Aggregate function which approximates the maximum function, is introduced, and data clustering problem is reformulated as the unconstrained optimization.

借助于近似极大值函数的凝聚函数，将传统数据聚类问题转化为无约束优化问题求解。

Starting from the graphs of P-V and T-S and the second law of thermodynamics, and on different aspects and with different methods, this article studies the maximum value of the efficiency of heat engine in the process of arbitrary cycles, and presents the conclusion that the efficiency of the heat engine in Carnot cycle is the greatest among all arbitrary cycles.

卡诺定理给出了热机的循环效率极大值问题。由P-V图、T-S图、热力学第二定律出发，从不同的角度，采用不同的方法，对任意循环过程的热机效率极大值问题进行了研究，证明了任意循环过程热机效率以卡诺循环的热机效率为最大极限值的结论

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。