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Linear programming problems generically involve the use of a repeated algorithm to solve. Is there a reason they can't be solved algebraically/formulaically?

Ex:

Minimize x1 + x2 + x3....

x1, x2, x3... >= 1

Has a solution (1,1,1...) for any dimension

With a little work we can extend this to include coefficients...

Is there a way to explicitly solve any LP? What proof is there that it cannot exist? What machinery would be needed before such a thing can be done

Sidharth Ghoshal
  • 16,771
  • I am not sure what do you mean by "explicitely". Do you think that there is a way to solve any linear system explicitely? If you would say yes, then there is also a way to solve any LP explicitely... – Dirk Jun 10 '13 at 15:07
  • Like given any quadratic you can just plug it into the quadratic equation and its done... The algorithm needs to be used one time... In a single stream of calculations – Sidharth Ghoshal Jun 10 '13 at 16:14
  • Can LP's be approached the same way? – Sidharth Ghoshal Jun 10 '13 at 16:14

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