Secondly , according to convex geometric characteristics , a common - perpendicular - line algorithm is developed for the distance between the convex nurbs surfaces by making surfaces discrete , approximating the distance by one between convex hulls of discrete surfaces and solving a linear programming problem to get their vertical projective length on common perpendicular direction , that is , the original distance 然后，针对凸曲面的几何特征，给出了nurbs凸曲面间距离求解的公垂线法和切平面法。公垂线法是把曲面间的距离求解问题转化成曲面的离散点生成的凸壳间的距离，再归之为两凸壳在其公垂线上投影集合间的距离，由此抽象成一个线性规划问题，估算出近点对。
In contrast to existing simplex method , this method has several peculiarities as follows : to begin with , applying it to solve linear programming problem . one need n ' t introduce any additional variable such as relaxing variable , artificial variable and other parameters , so that calculation is subtracted on a large scale . in addition to this , as a result of its higher degree of structuralization , this algorithm can be more easily transformed into program language and , of course , more quickly performed by computers 与现有的单纯形法相比，新算法具有如下主要特征：第一，求解过程不需要引进诸如松驰变量、人工变量等参变量参与运算，计算量大大减少了；第二，新算法较单纯形法的结构化程度高，更容易转化为程序语言，进而在计算机上更快地得以实现；第三，新算法在运算过程中不会引起摄动现象。
In section one , based on theory of n dimensional euclid space , a new method labeled as " pointlineplane " recycling optimization algorithm is proposed to solve the linear programming problem . this algorithm is proposed on the basis of the thought as follovvs : as for three dimensional euclid space , the feasible region of any linear programming problem is a extended convex polyhedron , of which surface is consisted of some planes , and its objective function can be regarded as a parallel plane pencil with objective function value acting as parameter 第一部分内容是在n维欧氏空间理论的基础上提出了一种求解线性规划问题的新算法? “点线面”循环寻优法，本算法是基于如下思想提出来的：我们知道，在三维欧氏空间中，线性规划问题的可行域是一个由若干个平面围成的广义多面体，目标函数可以看作是以目标函数值为参变量的一个平行平面束。
According to order relations defined between fuzzy numbers , the pareto less optimal solution and the pareto optimal solution are defined , then a fuzzy evaluation function is introduced into a multiobjective programming problem , this method results in a multiobjective programming problem been converted into a one objective programming problem , accordingly the solution by this method is the pareto less optimal solution to the primitive problem , which is given proof a multiobjective problem with general fuzzy number coefficients is also further discussed , by _ cutset of fuzzy sets a multiobjective problem can be transformed into a interval linear programming problem , and using the method of the previous chapter , we can obtain the pareto less optimal solution 从模糊数之间的序关系出发，分别定义了弱较优解和较优解，然后对模糊多目标问题引入模糊评价函数，将多目标化为单目标，在此也证明了求得的解为原问题的弱较优解。还讨论了系数为一般模糊数的多目标问题，通过模糊集的水平集可将多目标问题转化为区间数线性规划问题，并利用上一章所讲的方法，得到原问题的弱较优解。最后，对变量为模糊数的线性规划问题也进行了讨论。
