Understanding Linear Equations and the Simplex Method for Function Optimization

In summary, there exist many alternatives to the Simplex algorithm, but the Simplex algorithm is the best way to solve a Linear Programming problem.
  • #1
Pattielli
296
0
I would like to know if anyone of you can help me simplify the main ideas of the Simplex method used to optimize a function...Would you please help me ?

In case which I don't use Simplex to solve the problem, could you tell me if there exist to be any other methods that I can choose ?

Thank you very much,
 
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  • #2
Anyone can help ?

Thank you,
 
  • #3
Probably not. Your question is much too general. It would be better to post a specific problem. It would also be better to post it in "general math" rather than "linear and abstract algebra".
 
  • #4
Thank you very much...

It is just that i don't understand how to make a program that finds the optimal values subjecting to certain constraints, with a given objective function, there are lots of information on the net and in libraries but they are all hard to understand, they are written long and in a broad sense...I asked this question to only hope that someone who already dealed with these kinds of problems before could give me a more specific and understandable explanation for me to make a computer program...
There is also soure code on the net but I would like to code it myself...

Thanks for your suggestions, and I am sorry for having posted in a wrong forum...
 
  • #5
Pattielli said:
I would like to know if anyone of you can help me simplify the main ideas of the Simplex method used to optimize a function...Would you please help me ?

In case which I don't use Simplex to solve the problem, could you tell me if there exist to be any other methods that I can choose ?

Thank you very much,

There possibly are heuristic alternatives to the Simplex Algorithm, which can be developed in a case-by-case basis. Of course, they will give only sub-optimal solutions.

For a Linear Programming problem involving only 2 variables, there is a simple graphical solution. I'm sure you will find this in any basic Operations Research / Linear Programming text. This approach can also be extended to a 3 variable case, but it requires a good knowledge of 3D geometry - specifically how to find lines of intersection of 2 planes, etc.

In general, the best way to solve a LP problem is using the Simplex Algorithm - and of course, this works only for Linear problems and not for quadratic, cubic, dynamic (etc.) programming probles. Do not try to avoid the Simplex approach...it is very useful. Understanding the graphical approach could help you understand why Simplex works.

I'm sure this is covered in all Introductory Op. Research books.
 
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  • #6
Have you tried doing some simple simplex examples by hand so that you understand the method? From the way you're writing I suspect not. It is a simple method and if you looked at the teaching resources on say, www.dpmms.cam.ac.uk under the optimisation and control subjects you will get a clear explanation of how to implement it.
 
  • #7
Thank you Gokul43201 and Matt very much, I truly didn't see Gokul answer this thread of mine till Matt gave me that post...

Matt, yes, I actually didn't solve it by pencil and paper...(smile)

Again thanks both a lot,
Regards,
 
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1. What is a linear equation?

A linear equation is an algebraic equation that contains only variables raised to the first power and constants. It can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept.

2. How does the simplex method work for function optimization?

The simplex method is a mathematical technique used to solve linear programming problems. It involves creating a table of values and systematically adjusting the values to find the optimal solution for the given constraints and objectives.

3. What is the difference between a linear and non-linear equation?

A linear equation has a constant rate of change and forms a straight line when graphed, while a non-linear equation has varying rates of change and forms a curved line when graphed.

4. How do you solve a system of linear equations using the simplex method?

To solve a system of linear equations using the simplex method, you first need to convert the equations into standard form by adding slack variables. Then, create a simplex table and use the method of pivoting to find the optimal solution.

5. What are some real-world applications of linear equations and the simplex method?

Linear equations and the simplex method are used in various fields such as economics, engineering, and business to optimize resources and maximize profits. They can be used to solve problems related to production planning, resource allocation, and transportation logistics.

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