Linearprogramming conditions are unknown

Hello there, I need help figuring out how to set the paremeters for this specific linear programming problem:

including the function for L, and the conditions A, b ,Aeq, beq.

(whichever conditions I might have))

My thoughtprocess so far is that there is only one ineqality condition:

lb < L < ub ( lb = 0, ub = random integer)

f = abs(sum( m - L ));
A = [];
b = []; 
Aeq = []; 
beq = [];
lb = 0;
ub = j;

Sets are empty because I dont know how to discribe the parameters.

All information I do have is in the Text below.

the "easy" way to calculate L is to take the mean(m), but I must not use anything different then an optiization tool.

L = distance from the "Main Station" to the start of the Line ( point 0), which needs to be optimized.

% A railway line has n stations, with n  2. Each of the stations is at points xj 2 R,
% where j = 1; 2; : : : ; n, and the two ends of the line correspond to x1 and xn,
% respectively. We will assume that the following sequence x1 < x2 <    < xn holds.
% It is desired to locate the railway trac management center of that line at a point
% xc 2 [x1; xn] so that the total sum of the distances from the management center
% to each of the stations is minimal. Determine at which point/points xc 2 [x1; xn],
% along the railway line, should the trac management center be located and nd
% the minimum value of the distance in terms of the positions xj of the stations.

Thanks for your time, I hope this is not to much to ask for.

It would already help if you see any mayor mistake and point it out so I can specify my question more.

[Matt J]

the "easy" way to calculate L is to take the mean(m)

I think you mean median(m), since the objective is a sum of absolute values, not a sum of squares.

Answer 1

[Matt J]

As I mentioned in your previous post, you want to set up the following equivalent LP,

I don't think it should be a difficult exercise to write the A,b matrices required by linprog. However, you may also want to consider the problem-based approach to setting up a linear program.

[NIKLAS EHLERT]

Edit:

So I just randomly used the fminbnd, solver and it works. (I guess)

j = randi([1 1000]);
n = randi([2 20]);
m = randi([j],n,1);
m(1) = 0;
m(n) = j;
m = unique(m);
m = sort(m);


fun = @(L) abs(sum(m - L));


L = fminbnd(fun,0,j)

so ill use this now.

Edit,end

Hey Matt,

thanks for sticking with me.

Honestly its not that easy for me, converting text to Math-expressions and then to code is hard just beginning this journey.

Is it rude to ask for further help?

Trying to figure out what you mean:

L = distance to 0, but what is its function? ( 0+L ; doesn't make sense, i need to solve for L but my programm wants an input before, do I need to make 2 functions and import one into the other?)

r = function for sum, r = abs(sum(m-L)) ; where i ist the number of iterations?

constrains are:

0 < L < j

-sum(max L) < sum(m-L) < +sum(min L) (???)

what do the A and b look like?

n = number of stations (size of m)

A = ones([n,1])

b = ??? ; which constrains belong here?

I dont even know if these are A,b or Aeq,beq ; for not knowing if they are equal or not and if it makes a difference.

Thanks for youre time.

Cheers