1 / 14

The simplex method for infeasible solution

The simplex method for infeasible solution. Example. -x1-2x2+3x3<=3; -2x1-6x2+x5>=9; 3x1-x2-7x5>=2; x1+5x2+4x4>=5; x2-3x3>=6;. slack variables artificial variables. x1 x2 x3 x4 x5 s1 s2 s3 s4 s5 y1 y2 y3 y4 y5 b. Min Σ y i ≠ 0 → infeasible. For convenience:.

gonzalezh
Download Presentation

The simplex method for infeasible solution

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. The simplex method for infeasible solution

  2. Example -x1-2x2+3x3<=3; -2x1-6x2+x5>=9; 3x1-x2-7x5>=2; x1+5x2+4x4>=5; x2-3x3>=6; slack variablesartificial variables x1 x2 x3 x4 x5s1 s2 s3 s4 s5y1 y2 y3 y4 y5b Min Σ yi ≠ 0 → infeasible

  3. For convenience: ......(1)

  4. First pivoting(i) Suppose is chosen as pivot Eliminate from (1) by substitution: (*)

  5. First pivoting(ii) Eliminate from other rows by substitution: g ≠ i

  6. First pivoting(iii) (1)= Sum of each rows = sum of those rows not containing pivot Proof:

  7. First pivoting(iv) Similarly,

  8. Pivoting invariant(i) The last row = -1* (sum of those rows not containing any pivot) Proof:

  9. Pivoting invariant(ii) Ex:

  10. Terminal condition and infeasibility When simplex method terminates, the last row (equation) must be of the form: where It’s a contradiction!!

  11. UNSAT proof Ex: 768*(-2x1-6x2+x5>=9) 512*(3x1-x2-7x5>=2) -5120x2-2816x5>=7936 768*(x2-3x3>=6) -4352x2-2304x3-2816x5>=12544 4352*(X2>=0) -2304x3-2816x5>=12544 2304*(X3>=0) 2816*(X5>=0) -2816x5>=12544 0>=12544

More Related