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,
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".
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....
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.
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.
Thank you Gokul43201 and Matt very much, I truely 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,