What are the two methods of the simplex method?

In the large m method, m is an arbitrary large positive number. There is also a second-order method.

Simplex methodIt is one of the most commonly used and effective algorithms for summing ridge perturbation to solve linear programming problems. Its calculation steps are as follows:

1. The constraint equations of the linear programming problem are expressed as exemplary equations, and the basic feasible solution is found as the initial basic feasible solution.

2. If the basic feasible solution does not exist, that is, there is a contradiction in the constraints, then there is no solution to the problem.

3. If the basic feasible solution exists, take the initial basic feasible solution as the starting point, and introduce a non-fundamental variable to replace a fundamental variable according to the optimality condition and feasibility condition, and find another basic feasible solution with a better objective function value.

4. Iterate according to step 3 until the corresponding test number satisfies the optimality condition (at this time, the objective function value can not be improved), that is, the optimal solution of the problem is obtained.

5. If the objective function value of the problem is found to be unbounded during the iteration, the iteration will be terminated.

The concept of the simplex method: Summoning

The simplex method is one of the most commonly used and effective algorithms for solving linear programming problems. The simplex method was first proposed by George Dantzig in 1947, and over the past 70 years, many variants have been developed, but the same basic concept has been maintained. If an optimal solution to a linear programming problem exists, it must be found at the vertices of its feasible region.

Based on this, the basic idea of the simplex method is to find a vertex of the feasible domain of Yejing, and judge whether it is optimal according to certain rules; If not, it converts to another vertex adjacent to it and makes the objective function value better; And so on until an optimal solution is found.

Step 1: Based on the coefficient matrix of the system of constraint equations, by finding or constructing the identity matrix.

The initial basic feasible solution is obtained, and then the initial simplex table is compiled by using the initial basic feasible solution and the information provided by the linear programming model.

Step 2: Take the test number cj-zj as the criterion for judging whether the basic feasible solution is the optimal solution, 1) If the physical idea test number cj-zj <0 for all non-fundamental variables has reached the optimal solution, the calculation will be stopped.

2) If there is cj-zj>0, but all AIJ 0 corresponding to all cj-zj>0 columns, there is no optimal solution, and the calculation is stopped.

3) If there is at least one cj-zj>0 in the manuscript, and there is at least one aij>0 in all the corresponding j columns, and the optimal solution is not reached, go to the third step.

In the objective function, a non-fundamental variable is used instead of a fundamental variable, and the resulting coefficient is the test number.

In the world of target planning, p1p2p3 is not a specific calculated value, but according to the original method on the straw paper to write the formula for calculating the check number, the coefficient has p1p2p3 with it, and the finishing will get a formula about p1p2p3, and the column is filled in the coefficient of p1p2p3 in this formula, so you can fill in one column after another.

The specific steps of the simplex method are to find a simple shape from the system of linear equations, and each simple can obtain a set of solutions, and then judge whether the solution increases or decreases the value of the objective function, and determines the simplex to choose in the next step. Iterate through optimization until the objective function achieves a maximum or minimum value.

As a mathematics student, I didn't write a summary of mathematics, and I was taking a research class and learning the simplex method.

So I'm going to write about his solution.

As we all know, there are many ways to solve a linear programming problem, and we apply a similar enumeration method.

It is possible to solve the problem when the number of basically feasible solutions cm,n, but if the number of feasible solutions increases, we are faced with the following three problems that must be solved quickly:

Workaround:1**The first row is for all the coefficients of the objective function variable.

2.**The second line, the left part, has three items: CB, XB, and B. The right part, which is all variables (including basic variables, residual variables, relaxation variables, and artificial variables).

3.**The last line, the calculation of the objective function: the objective function coefficient of the variable cb * the coefficient of the constraint function variable, and then sum.

4.In the middle rows, the right part is the coefficient of each constraint function. The determination of the xb of the left part is based on the occurrence of the right part of the identity matrix.

of the coefficient begins to record its variables. cb is the coefficient in the objective function of xb. b is calculated when all variables (except xb variables) are 0.

Artificial variables: To maximize our objective function, artificial variables must be quickly swapped out of the base variables, otherwise the objective function cannot be maximized.

There are two ways to solve: minimize and maximize.

There are certain differences between them, and the above methods are used to maximize the solution.

Minimization Discussion Early Problem Solving: The base selects the one with the smallest negative discriminant number to reach the optimal solution when all discriminant numbers are greater than or equal to 0.

The maximization problem is solved: the base variable selects the largest number with positive discriminant numbers, and achieves the optimal solution when all discriminant numbers are less than or equal to 0.

Commonality: The off-base variables are all taken with the smallest ratio.

1. Simplex method:

1. Advantages: The constraint equations of the linear programming problem are expressed as a system of exemplary equations, and the basic feasible solution is found as the initial basic feasible solution. A numerical method for optimizing multidimensional unconstrained problems, which falls into the category of more general search algorithms.

2. Disadvantages: There are constraints greater than or equal to those in the constraints: the constraints will be negative on both sides of the constraints.

Second, the ** law:

1. Advantages: The principle is simple, easy to grasp, and it can be used if you can count the grids.

2. Disadvantages: the accuracy is limited, it is best to accurately calculate the integrals in the squarer or high numbers, and the ** method is suitable for use in some occasions where the accuracy requirements are not high.