Convex: Local vs Global Minimum

[@MathVisualProofs]

Nice one here. Really enjoyed it. Clear description of convexity.

[@ProfOmarMath]

Awesome!

[@aashsyed1277]

Hello there you Micro....

[@route66math77]

Fantastically explained, Dr.! Bursting with lucidity -- cheers!

[@ProfOmarMath]

Thanks, much appreciated!

[@yoav613]

Very nice.you used this property in your videos in the past,but it is nice to watch special video with detailed explanation about it

[@ProfOmarMath]

Ya about convex sets!

[@deepjyoti5610]

I like definition of convexity

[@ProfOmarMath]

Me too

[@abdulazizmemesh2791]

Your approach seems to have a circular logic. When you introduced z, you made up an inequality that we know holds for some t (the t's that makes our expression equals something inside that small interval). However, it has to be true for all t, which we can't prove is right. Therefore, the conclusion you have is not always true since you based it off of an inequality that is sometimes true. I'm not totally convinced by the proof. Let me know if I overlooked something.

[@AKapich]

I have the same notion, the proof here doesn't work (what if t is very close to 0 and tx^* • (1-t)z doesn't fall within the vicinity of tx^* ?)

[@NedSar85]

I enjoyed this so much! thanks

[@suvamkumarsahoo4462]

Define fk(n) to be the sum of all possible products of k distinct integers chosen from
the set {1, 2, . . . , n}, i.e.,
fk(n) = X
1≤i1

[@suvamkumarsahoo4462]

I get this question from my entrance exam of CHENNAI MATHEMATICAL INSTITUTE (Once search about it).

[@yaseengarehmohammadlou9349]

Another amazing video.thanks ProfOmar.my method is to use contradiction.the local minimum is not global so there is a another point which is global.so the line segment between them can not have an intersection with the graph but it has so it contradict the convexity of the graph.a friend of mine which had a operations research course asked me that anf I said this.i hope it is true.

[@ProfOmarMath]

Great to see you Yaseen! I think the part I have to think about is why the segment between the local and global min have to intersect the graph. Picturing a parabola hmm

[@yaseengarehmohammadlou9349]

@@ProfOmarMathI am know thinking it is better to say that a part of the segment is above the graph and a part of it is below the graph and with the definition of convexity it is a contradiction.

[@ProfOmarMath]

@@yaseengarehmohammadlou9349 Ah I see because near the local min it’s above but at the global min it’s below, ya!

[@yaseengarehmohammadlou9349]

@@ProfOmarMath sir I really enjoy your videos and learning from you.thkanks for the time that you send to answer the questions.you are one of the best teacher that I have ever had.

[@tonyhaddad1394]

Great video !!❤❤❤

[@ProfOmarMath]

Thanks!

[@tonyhaddad1394]

@@ProfOmarMath ❤❤❤

[@thewolverine7516]

When will you be posting content again? Please reply.

[@PikasoCapture]

never

[@thewolverine7516]

@@PikasoCapture why? How do you know?

[@PikasoCapture]

@@thewolverine7516 he left youtube

[@thewolverine7516]

@@PikasoCapture Well tell me how do you know?

[@ggg9gg]

@@thewolverine7516 he told him

[@rounaksinha5309]

Hello sir, how are you doing?

[@ProfOmarMath]

EduHub! How’re you? I just had surgery yesterday. Hopefully it helps

[@rounaksinha5309]

@@ProfOmarMath Hello sir ! I am doing good. I ended my semester 1 with nice perecentage.Sir,I hope that the surgery that you undergone helped you . Sir we pray to god that you recover soon.
Sorry for poor english sir.
Have a great day sir !

[@rounaksinha5309]

Just love you sir.You are very kind ! I will also try as best I can to become a nice professor like you.Please bless me sir !

[@ProfOmarMath]

@@rounaksinha5309 I’m happy your semester went well and thank you so so much!

[@ProfOmarMath]

@@rounaksinha5309 Amazing!