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Can Linear Programming Simplex Method VI solve the optimization problem with real value variables (x>=0 or x<0)? If yes, how?

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Hi, Thanks for your reply. But in the guidance you provided, Linear programming Simplex Method VI is only used for nonnegitive variables, i.e., x>=0. I am wondering whether the VI can be used for both negative and nonnegative varibales or not. Any suggestion with more details? Thanks a lot.

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Solution
Accepted by topic author ZDX

Assuming your (potentially) negative variables have constraints (say -1000) you can offest them accordingly and adapt your input data correspondingly.

 

replace x0 >= -1000 with X0 = (x0 + 1000) >= 0

 

Don't use negative constraints unnecesseraly big as it may results in numerical issues.

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Solution
Accepted by topic author ZDX

I've created a quick example (Lv2014) that finds the minimax solution for three equations with two variables.

The solution has both variables negative so using the raw algorithm returns {0, 0}. If you increase the variables offset parameter, the actual solution { -4.86. -0.49} is found for any offset value >= 4.87.

 

I hope this works for you!

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Thanks for your help. It works for me! 

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