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

In summary, the conversation discusses the relationship between primal LOP K and dual LOP D. If D is bounded, meaning it is feasible, then it can be concluded that P, which is equivalent to K, is also bounded. Similarly, if D is unbounded, then P will be infeasible. The conversation also mentions that the letters K and P refer to the same thing, while D is used to represent the dual LOP. Linear Programming is mentioned as a possible expansion for LOP, but the meaning of the "O" is unknown.
  • #1
flyingpig
2,579
1
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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  • #2
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??
 
  • #3
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.
 
  • #4
And LOP? I know what it means, but it would be helpful to other readers if you expanded this acronym once.
 
  • #5
Linear Programming.

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

Sorry for the confusion.
 

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

What is the Weak Duality Theorem Theory?

The Weak Duality Theorem Theory is a mathematical concept used in optimization theory, specifically in linear programming. It states that the optimal solution to the dual problem is always less than or equal to the optimal solution of the original problem.

How is the Weak Duality Theorem proven?

The Weak Duality Theorem can be proven using the fundamental theorem of linear programming, which states that the optimal value of the primal problem is equal to the optimal value of the dual problem. This can be shown through the use of mathematical proofs and equations.

What is the significance of the Weak Duality Theorem?

The Weak Duality Theorem is significant because it allows for the simplification and understanding of complex optimization problems. It also helps in determining the feasibility of a problem and can provide a lower bound for the optimal solution.

What are some real-life applications of the Weak Duality Theorem?

The Weak Duality Theorem has various applications in fields such as economics, engineering, and finance. It can be used to find the most efficient allocation of resources, determine the best production levels for a company, and optimize investment portfolios.

Are there any limitations to the Weak Duality Theorem?

While the Weak Duality Theorem is a useful tool, it does have some limitations. It only applies to linear programming problems, and it assumes that the problems have optimal solutions. Additionally, the theorem does not provide a method for finding the optimal solution, just a lower bound.

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