Problem, so, um, suppose you have a given and a plain triangle and you want to find out the point
like X and Y in a way not the sum of its distances to the vertices of the triangle is minimal.
So we are assuming that the coordinates of the triangle are already known.
So the location of A, B, C points are known.
And what we want to find is X and Y.
So we want to minimize the one, for example, let's say the one D two and three, some together and
also and in order to find the value of each distance, the following formula can be used.
LDI Square is equal to X minus X squared, plus Y minus Y square.
So X and Y are the coordinates of the triangle.
OK, so in order to solve this problem, we have to know which parameters are known.
X I Y are known and the decision variable are X and Y, so um less formulated in Palermo.
First of all, we need to, um, let's say, um, import some libraries, OK, for example, the Palomo
Library, matplotlib, M.P. and a random, um, package, OK, and then we have to create a model,
for example, let's say model, concrete model.
And, um, let's assume that if we have a triangle like this and if the first, um.
Waters of the triangle is located on the Origin 010, another one is called A and the other one is called
B.
OK, so we want to first of all, specify the and B and then and there are two variables called X and
Y.
These are the coordinates of that central point and F one is the objective.
So you can see here a model that F one is objective and the description is as follows.
OK, so we want we can and do the summation one by one.
So this one is the D one is Q are of model X minus zero square plus a model Y minus zero square.
You are T between X and zero B.
Oh so it's here zero and B sorry.
It's here.
X is zero, Y is Bidya, and also the last one, this is the point, A Hmm.
So the distance between that point and Point A is calculated here and the sense of the optimization
is the minimization.
OK, so like every other optimization problem, we do have to specify the solver, which is EPOP here
for obvious reason because it's non-linear programming.
Then we have to ask and Palomo to solve the problem for us and the results are saved here.
Let me run the problem here.
So this one is run successfully.
This top is run next and this one also is done.
And also, if I run this, you can see the values of X and Y are found, the optimal values are found
and or objective function is also, uh, calculated.
OK, if we want to show it visually, then you can easily see that how they are scattered here.
OK, so this is the, um, point.
We are looking for it.
OK, thank you very much.
And this is the example regarding the, um, Steiner problem.
Thank you very much.