About Farkas Dual in Benders Decomposition

Answered

Fan YANG

• October 17, 2019 10:36
• Edited

Dear,
I am working on a Benders Decomposition, and I would like to add feasiblity cuts to master problem by Farkas dual. I have several problems as:

1.  The value returned by the call of farkas dual isn't the extreme ray of the dual problem of the sub-problem?

2. The primal sub-problem is minimziation. The right hand of the sub-problem is "(B - Dy)" . I added " 0 >= r * (B-Dy)" to the master probelm, where "r" is obtained by fakas dual. But I cannot get the right solution. When I added " 0 >= (-1) * r * (B-Dy)", then the solution is right. Do you konw the reason for this?

3. Sometimes the result of r * (B-Dy) is negative, sometimes it's positive? what's the reason for this?

 

Many thanks,

Related to

• Bender's

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• 

  Thomas Opfer

  • October 17, 2019 15:37

  

  

  1. The returned vector is the Farkas Dual of the problem where it is returned from. (Obviously.)

  2./3. Do you have variables with non-trivial bounds? If yes, please read this (including the comments) in order to find out the differences between Farkas Dual and the dual ray.

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  Fan YANG

  • October 24, 2019 15:11

  

  

  

  Hi Thomas, 

  Thanks for your reply, I am trying read and learn that page.

  Best.

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• 

  Simin Chai

  • November 21, 2023 02:13

  

  Hi Thomas, 

  The link you provided above does not work, and I can not access the line/website.

  Could you please provide the new reference?

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  Riley Clement

  Gurobi Staff

  • November 21, 2023 02:15

  Hi all,

  For what its worth I can access the link that Thomas posted.  Simin, perhaps your internet traffic is being restricted and a VPN would help?

  - Riley

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  Simin Chai

  • November 21, 2023 02:27

  

  Hi Riley,

  Thanks for your reply.

  It is my internet problem. The link is valid.

  Best

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