What is Linear Programming (LP)? (in 2 minutes)

[@prolixescalation1932]

Ahhh, so nice to see this video while I'm taking classes about methods of optimization

[@tanishqawasthi5664]

It's so great to see someone taking out time and doing efforts to make us understand optimization better in visualisation....kudos to you.... Please make more videos on optimization including topic like duality, Non-Linear optimization and constraint Non linear optimization and on Neural network as well...

[@VisuallyExplained]

Much appreciated! More videos on optimization are coming...

[@BrianAmedee]

So this is a code that optimises stuff based on constraints? Nice. Straight to the point, well done

[@mayureshjoshi4616]

Wow simply awesome , visuals were awsome and so are you!!!

[@aleocho774]

Here from Ahmad Bazzi 's NVIDIA video. Awesome stuff mate.

[@VisuallyExplained]

Thanks a lot mate!

[@philippvetter2856]

I love these videos. These are amazing explanations and really helpful for people that are new to optimization!

[@VS-wq3ws]

Super informative video with visualisations Thank You from india

[@jayantnema9610]

dat tax evasion line! ☠️☠️☠️

[@patakhte6367]

Thank you. So useful and intuitive.

[@siddharthvm8262]

Amazing work. Please go on

[@PeekPost]

Video visually showing comparison between simplex on kkt and IP on kkt (along with their performance) would be great!🤠

[@hbasu8779]

Thanks for explaining it so well. I had a question: why in LP the optimal solution is found at one of the vertices of the polyhedron ( feasible set) ?

[@Schnorzel1337]

That is indeed not the case. There can be no solution (feasible set is empty), uncountable infinite solutions (feasible set is not completely bounded), infinite solutions (all the solutions on a edge between two points) multiple solutions (one solution per vertex). For your question: Lets say we have a feasible set where the optimal solution is on one of the faces of the polyhedron. Which means there is a vector from (0,0,0) to the optimal point (x,y,z) of optimal length n. Now every point on the plane has to be closer to the origin than our point (x,y,z), which is striclty impossible, unless the plane is curved, which by definition is never true. Furthermore any point inside the feasible set is clearly not optimal, because the vector could stretch through that point until it hits the boundary. With those 2 ideas in mind you can see that every optimal solution is on a vertex or on the edge between two vertices.

[@vTutorLive]

Great work! It's been a few years since I've done LP, but it would have been nice to have a visual as sharp as this when I first learned it. I actually wasn't familiar with "strongly" polynomial time (as opposed to just polynomial time). I'm sure these videos are made with brevity in mind, but consider putting a quick, informal definition off to the side? Unless I just missed it

[@VisuallyExplained]

Thanks for watching! You make a good point. I have added more details about the distinction between polynomial and strongly polynomial time algorithms. The definition is somewhat technical, but the basic idea is that a polynomial time algorithm is allowed to take more time as the magnitude of the coefficients grows (while keeping the number of variables/constraint constant), but a strongly polynomial time algorithm is not. The interior point method is a polynomial time algorithm, but not a strongly polynomial time one.

[@hyukppen]

Is the semidefinite programming different from the linear programming? It seems similar but I don't understand the difference.

[@VisuallyExplained]

Fantastic question! I have a feeling you will be interested in the next video coming up :-)

[@hyukppen]

@@VisuallyExplained Oh, I will wait your next video. Thanks.

[@AK56fire]

Beautiful animation.. Please make a making video tutorial for the part that you did in Blender.

[@matthewjames7513]

nice vid but plz no dubstep nextime

[@VisuallyExplained]

Thanks for the feedback. The background music turned out a bit more distracting than I had anticipated indeed.

[@JoelRosenfeld]

@@VisuallyExplained I enjoyed it

[@michael-nef]

lol, solving the second open question is equivalent to solving the P=NP conjecture.

[@VisuallyExplained]

While the two questions sound similar, there is a priori no direct relationship between the two. For all we know, someone could prove that a variant of the simplex method runs in strongly polynomial time, and we would still have no clue about P=NP.

[@子不語-e8y]

Could you add english caption so that it make easier for foreigner

[@VisuallyExplained]

Thanks for the suggestion! In my experience, the automatically generated captions are pretty good. Let me know if you still have problems with that and I will consider adding custom captions.

[@bigbuckey7687]

Great production value, horrendous music.

[@ashraf_isb]

tax evasion 😅

[@Piipolinoo]

Whats up with that horrible music in the background? the fuck