摘要：一、基本思想：从线性规划问题的一个基本可行解出发，判断其是否为最优解，若不是，则转换到相邻的基本可行解，并使目标函数值不断增大，直到找到最优解或判断无界为止。
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一、基本思想：从线性规划问题的一个基本可行解出发，判断其是否为最优解，若不是，则转换到相邻的基本可行解，并使目标函数值不断增大，直到找到最优解或判断无界为止。
1. Basic idea: Starting from a basic feasible solution of the linear programming problem, judge whether it is the optimal solution, if not, convert to the adjacent basic feasible solution, and make the value of the objective function increase until the optimal solution is found or judged to be unbounded.
二、步骤：
2. Steps:
1、标准化：将线性规划问题化为标准型，引入松弛变量、剩余变量和人工变量等，使约束条件变为等式，目标函数变为求最大值。
1. Standardization: The linear programming problem is turned into a standard type, and relaxation variables, residual variables and artificial variables are introduced, so that the constraints become equations and the objective function becomes the maximum.
2、确定初始基本可行解：一般可根据标准型的系数矩阵确定，如松弛变量对应的列向量构成单位矩阵时，令松弛变量为基变量，非基变量为0，得到初始基本可行解。
2. Determine the initial basic feasible solution: Generally, it can be determined according to the standard coefficient matrix, for example, when the column vector corresponding to the relaxation variable constitutes the identity matrix, let the relaxation variable be the base variable and the non-basis variable be 0 to obtain the initial basic feasible solution.
3、最优性检验：计算检验数，若所有检验数小于等于0，则当前基本可行解是最优解；若存在检验数大于0，则目标函数值还可增大，该解不是最优解。
3. Optimality test: calculate the number of tests, if all the tests are less than or equal to 0, the current basic feasible solution is the optimal solution; If the number of tests is greater than 0, the value of the objective function can be increased, and the solution is not optimal.
4、基变换：选择正检验数中最大的对应的变量为进基变量，通过计算确定出基变量，进行初等行变换，得到新的基本可行解。
4. Basistransformation:Selectthelargestcorrespondingvariableinthepositivetestnumberasthebasevariable,determinethebasisvariablethroughcalculation,andcarryouttheelementaryrowtransformationtoobtainanewbasicfeasiblesolution.
5、重复最优性检验和基变换：不断重复上述步骤，直到找到最优解或发现目标函数无界（当进基变量的系数列向量非正）。
5. Repeat the optimality test and basis transformation: Repeat the above steps until you find the optimal solution or find that the objective function is unbounded (when the coefficient column vector of the base variable is not positive).
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部分参考内容来自百度
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