So welcome everyone to today's seminar.

We have Professor Alexander Martin, who is both at FRO and at the Pound Offer Institute

for Integrated Seconds.

And then today he will be speaking about MIP and PD optimization in the context of caste

network optimization.

Professor Martin, you have the floor.

Thank you very much.

So I was so bold to put the word PDE in my title, although I have no idea of PDEs and

there was this expert sitting here.

Nevertheless, I did it for particular reasons and I will show you this during my talk and

I especially will talk a lot about the corporate research center that we run now in in Alang

and Darmstadt in Berlin for almost eight years.

And I will show you some of the results, not the newest ones.

So many of you might know already a lot of the slides, but nevertheless, I would pay

attention to a couple of things that I think still play an important role even now in our

consortium and also maybe in the future.

So as you all know, I'm not a PDE.

I'm the MIP guy on the left and I have two examples for you.

And you see here the first example and it's a typical network flow situation.

Now you have a graph.

You see here the lines or the blue lines are edges and you have intersection nodes and

you have these green and red dots which are sinks and forces in this network.

And those of you who come from my field and got all the classes from linear and combinatorial

optimization, it's a mixed integer network flow problem.

And these problems typically are easy to solve in the linear setting.

But now the flow in this case is gas.

And also we motivate typically our min-cost flow setting with water or gas in a pipe.

It's actually true that our network flow modeling has nothing to do with the physics in such

networks.

So the question of course from our point of view, how do you deal with such physics?

And here comes the physics and there are more experts here that can explain the first three

equations.

So the physics are internally continuous and in the system.

And our PDEs, these are the Euler equations, so part of it, or in some sense also in a

way that we currently cannot deal in completely in 3D as far as I understood, but you can

correct me.

So this is on one side you have these PDE world, on the other you have these discrete

decisions.

So you have variables that are elements that you can switch on and off like valves or compressors.

And this can be in all different kinds of ways you can do that.

Because there's a real combinatorial involved.

And you cannot dispense with one of them.

So whenever you neglect one of them, you really lose one core issue of this problem.

And this is actually true for guys.

You see here also inside such a pipe.

So this friction loss because of the friction in that pipe, you directly see it here that

plays a role.

And also if you look at the other picture, these networks could be complicated.

So another situation, but basically the same thing, another network flow problem.

Sorry, sorry Alex.