CODEWITHSUNDEEP
matlabexpressionminimize
Mitul Mundra
Mitul Mundra

Reputation: 1

Writing summation expression in Matlab

How do I write an expression in Matlab code involving summation of a variable and then how do I minimize the expression? ex. I need to minimize the following function

E= \sum_{i,j}[C_{ij}(r_{ij}) + C2_{ij}(r_{ij})^2]

I need to minimize the above expression for any values of r_{ij}s where i and j vary.

I could use the fmincon() in MATLAB but I am unable to write my expression suitably to give it as input to the fmincon().

Thanks.

Upvotes: 0

Views: 1943

Answers (2)

Egon
Egon

Reputation: 4787

fmincon and other optimization functions do not require you to write everything as an expression, they can optimize for functions as well.

function E = criterion(r, C, C2)
  e  = C.*r + C2.*r.^2;
  E  = sum(e(:));

I'm not completely sure about the syntax required by fmincon, but I guess it's something like E = f(theta), where theta is a parameter vector you want adjusted such that E is minimal. Since I don't find your problem clearly described, I will assume your parameters are C and C2 (in the case that r are your parameters, the case is similar and simpler).

As fmincon uses a vector to store the coefficients, we need a function that takes such a vector and transforms it into the sizes required by the criterion function above.

function E = criterionRolledC(theta,r)
  assert(numel(theta)==2*numel(r), 'The size of theta has to be twice the size of r');
  [M N] = size(r);
  C  = theta(1:M*N);      
  C2 = theta(M*N+1:end);
  C  = reshape(C , M, N);
  C2 = reshape(C2, M, N);

  E = criterion(r,C,C2);

That way, you can make an anonymous function that easily conforms to the interface of the optimizer: @(theta)(criterionRolledC(theta,rValues)) will do when the variable rValues in your current workspace contains your r values.

In case you want the exact opposite, i.e. your parameters are r, it is simpler:

function E = criterionRolledR(theta,C,C2)
  assert(numel(theta)==numel(C), 'The size of theta has to be the same size as C');
  assert(all(size(C)==size(C2)), 'C and C2 need to have the same size');
  [M N] = size(C);
  r = reshape(theta, M, N);

  E = criterion(r,C,C2);

And you can construct an anonymous function similarly to the other case.

Upvotes: 1

foglerit
foglerit

Reputation: 8269

Try this:

E = sum(sum( C.*r + C2.*r.^2 ));

where C, C2 and r are matrices of the same shape.

Upvotes: 1

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