Is a Bounded Dual Linear Program Indicator of a Feasible Primal?

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Discussion Overview

The discussion revolves around the relationship between boundedness in dual linear optimization problems and the feasibility of corresponding primal problems. Participants explore whether the boundedness of a dual linear optimization problem indicates the feasibility of its primal counterpart.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant suggests that if the dual linear optimization problem (D) is bounded, then the primal problem (P) must also be feasible, implying a relationship between the two.
  • Another participant points out that if the primal problem is unbounded, then the dual must be infeasible, supporting the initial claim.
  • There is a clarification regarding the notation used, with participants confirming that K and P refer to the same primal problem, while D consistently refers to the dual.
  • Participants express confusion over the acronym "LOP," with one participant providing the expansion as "Linear Programming" but noting uncertainty about the meaning of the "O."

Areas of Agreement / Disagreement

The discussion contains some agreement on the relationships between boundedness and feasibility, but it remains unresolved whether the initial claim about the implications of boundedness is universally accepted.

Contextual Notes

There are limitations in clarity due to the use of acronyms and notation that may not be universally understood, which could affect the discussion's accessibility.

flyingpig
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Say I have a primal LOP K and a dual LOP D

If D is bounded, which means it is feasible, does that mean P is also bounded?

Because if P is unbounded, then D is infeasible

Likewise if D is unbounded, P is infeasible

So D is bounded, P is feasible? Make sense?
 
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You might get a response of you weren't so cryptic. LOP? Also you start out with things named K and D, but later you have P and D - I assume K and P are the same??
 
mathman said:
You might get a response of you weren't so cryptic. LOP? Also you start out with things named K and D, but later you have P and D - I assume K and P are the same??

They are. K = P, and D = D...

I don't know why I switched letters sorry for the confusion.
 
And LOP? I know what it means, but it would be helpful to other readers if you expanded this acronym once.
 
Linear Programming.

I actually do not know what the O stands for...

Sorry for the confusion.
 

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