Linprog error - The number of rows in A must be the same as the number of elements of f & Error in [x fval] = linprog(f,​A,b,Aeq,be​q,lb,ub);

Hi , I am trying to do a linprog optimisation by referring to the example in Matlab. I need help to solve the errors. Ty.

my code is:

variables = {'e1','e2','p1','p2','a','c','k','m','y','z'};

N = length(variables); 

% create variables for indexing 

for v = 1:N 

     eval([variables{v},' = ', num2str(v),';']); 

end

% Lower Bound Constraints

lb = zeros(size(variables));

lb([e1,e2,p1,p2]) = [14.4,14.4,26.4,28.8];

% Upper Bound Constraints

ub = Inf(size(variables));

ub([e1,e2,p1,p2,k,m]) = [48,48,84,84,2.5,2.5];

% Other Constraints

A = zeros(2,4);

A(1,k) = 1; A(1,e2) = -1/36; b(1) = 1.7;

A(2,m) = -1; A(2,p2) = -1/36; b(2) = 1.7;

Aeq = zeros(2,4); beq = zeros(2,1);

Aeq(1,[a,e1]) = [1,-7/30];

Aeq(2,[c,p1]) = [1,-7/60];

% Objective function

if a <= c

      y = a;

else

      y = c;

end

if k <= m

      z = k;

else
    z = m;

end

f = z*y*24768;

% Solve the Problem with linprog

[x, fval] = linprog(f,A,b,Aeq,beq,lb,ub);

for d = 1:N

fprintf('%12.2f \t%s\n',x(d),variables{d})

end

fval;

[Geoff Hayes]

Lee - can you describe the problem that you are trying to optimize? For example, which function are you trying to minimize (this would be your f) and subject to what constraints (this would be your A)? The error message is telling you that because you have two rows in your matrix, then your f has to be a 2x1 matrix as well as per an example from linprog.

[lee yz]

actually I'm trying to do optimization to get the value of e1,e2,p1,p2 that can give the highest value of f.

My f formula is f = z*y*24768

My constraints are

14.4<= e1 <48 , 14.4<= e2 <48 , 26.4<= p1 <84 , 28.8<= p2 <84

a = e1/36 , c = p1/36 , k = 7(e2)/30 -1.7 , m = 7(p2)/60 -1.7

y is the lowest value between a and c

z is the lowest value between k and m

if z more than 2.5 then use z=2.5

Thank you. This is my first time using the optimization so I'm not familiar with the coding.

Answer 1

[John D'Errico]

Um, your objective is a product of z and y, which are in turn derived from the parameters.

This is NOT LINEAR programming. linprog will not be able to solve your problem as you have posed it.

[lee yz]

Thank you for your comment. Is there any other way I can do this optimization?

[John D'Errico]

The objective is nonlinear, so fmincon springs to mind as the obvious initial choice.

However, the way you have it set up, so for example, y is the smaller of a and c makes the problem non-smooth. So fmincon will probably fail. At best, it will be inconsistent. Your next question would be why does fmincon not work here?

Having said that, the next choice would be a stochastic optimizer of some ilk. For example, possibly consider a genetic optimizer, or perhaps a particle swarm tool. Those methods are often more robust to the problems that will cause fmincon to fail.

[lee yz]

Can you recommend me any good examples of related particle swarm optimization? I need some references to do this because I'm not familiar with coding. Really appreciate with your help. Thank you.

[John D'Errico]

I can't really help you a lot there. But if you are willing to try using linprog, why not try using a tool like this one:

http://www.mathworks.com/matlabcentral/fileexchange/7506-particle-swarm-optimization-toolbox

A simple search on the FEX shows literally dozens of those tools.