Operations Research 05C: Weak Duality & Strong Duality

Textbooks:

In this video, we'll talk about weak duality, strong duality, and how to use duality to solve the dual based on the optimal solution to the primal.

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[YongWang]

Hi Guys, please comment and let me know what you think about this Operations Research Open Course. Your feedback is really appreciated. If you enjoy the video, please subscribe and share. All my replies here are only related to the content in my own videos. I am afraid I won't be able to answer other questions. Thanks for your understanding.

[zoedesvl]

Just a random guy who wants to tell you that I thought my operation research was done but with your help I got an A in the end and what's more important, I do understand these theories. I cannot thank you enough.

[YongWang]

Correction: At 7:00, I forgot to add the inverse "-1" for the matrix B [1 1 8; 0 1.5 4; 0 0.5 2] at the bottom left corner

[jdt]

Yong Wang, you are an outstanding teacher! I keep having one aha moment after another. Thank you so much!

[shafiqshams]

The graphical explanation is outstanding.
Thank you so much!

[RanjeetKumar-nhcn]

Thank you sir ..!
It is very useful for me
And you forgot to write inverse but you have written in your comments
Thank you ...!
Have a great day ...!

[nourhanelzoghby]

Are you solve last example by big-M method?? Because you add artificial variables a2 and a3??

[TheJohannes]

What if the Primal is written in min and the dual therefore in max. Does this make the weak theorem different? Should it say c^Tx>b^Tv?

[riccardovalsecchi]

how can you find the optimal solution for the dual with three variables? can i compute it with graphical solution?

[wigginskuang]

Hi Professor Wang, could you please explain what is the M in the strong duality part? (where you said that when the constraint is = in primal, ui=coeff of si in R0-M)

[Ivon_vlog]

What’s the meaning of e2 in the title of the column?

[thanhphan]

I have a question: How are ai, j and aj, i different from one another? I watched the Dual and Primal video and understand how to derive dual from the primal but don't understand this expression in the standard form. Thank you in advance!

[fadygeorge]

there is an error in minute 7:00 in matrix multiplication
the result is incorrect and i think you choose matrix B by mistake !
we should choose matrix from the primal optimal table but for the initial basic variable which we start by in the initial table

[CarlosMatamala]

One question: Are the weak and the strong duality theorems valid only for linear problems?