Welcome back to our pattern recognition Q&A.

I've received again many of your questions and I selected a couple of those to be replied

to in this video.

And today's video will be all about convex optimization, Lagrangian mechanisms, Lagrange

formulations and things, concepts like strong duality.

And I've picked a couple of very simple examples which I hope will help you understanding those

rather mathematical concepts.

So looking forward into discussing some examples for convex optimization, Lagrangian optimization,

regularization and strong duality.

Okay, so I prepared this small set of slides and I summarized some of your questions.

And then again, we are talking about pattern recognition machine learning.

You know, it can always get worse.

Imagine that you would be dealing with things like described in this book here.

So don't worry about it.

We'll get there and I'm making this Q&A videos such that you can understand the mathematics

that we're discussing here in much better detail.

So again, popular questions.

Something that occurs quite frequently is emails like this one.

I want to work in your lab.

Pretty pretty please.

Do you have a job?

Can you give me a PhD topic?

Can you supervise me and so on?

Can you hire me?

And unfortunately, it's rather hard to find a job in tech and it's not like that we don't

have any applications or something like this.

So it's pretty competitive to find a good position and you know, one does not simply

find a job.

But what if I told you that we can actually help you with finding a position?

So we actually have quite a few social media groups and in particular on LinkedIn and Facebook,

we regularly post also job offers there, not only with us, but also with our partners.

So if you're looking for a position, maybe also a PhD position, we publish those things

always in our social media groups.

So don't send just your CV to me, but you can join the groups.

I will post the links here in the description of this video.

And we are publishing positions for assistant jobs at our university, for PhD positions,

for postdoc positions, and we even have sometimes positions for professors, not just in our

group, but really in our network collaborators all around the world.

And we will post them there.

And you are of course welcome to join those groups.

And if you find something that you think is a good match, then send your CV and don't

take an effort of just sending CVs out there to everybody.

It's not very likely that we will have a position that is not advertised in this group.

So if Nick Cage can still get work, then you can do anything.

Keep that in mind.

Okay, so let's go to the actual topic.

We want to discuss a bit what convex optimization is and why it's important.

And you know, this is a convex function here, y equals x square.

And the cool thing about this is if we do a minimization here, it doesn't matter if

we start here, follow the negative gradient direction, we end up here.