Writing equations in a matrix form
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Hi MATLAB experts,
Could any one please help me to write-down the following equations into a matrix form? the initial value of c = zeros(I, L, K, M)
0<= c(i, j, k, m) <= 1 for all k= {1, 2, ...., K} and m = {1, 2, ..., M} and i = {1,...., I} and j = {1,..., L}
0<=sum_{j} sum_{i} c(i,j,k,m) <= 1 for all k= {1, 2, ...., K} and m = {1, 2, ..., M}
4 Comments
Walter Roberson
on 19 Apr 2019
The first set of conditions you would normally express through lb / ub matrices, unless you were using Problem Based Optimization.
Walter Roberson
on 19 Apr 2019
Edited: Walter Roberson
on 19 Apr 2019
Yes, those should be okay lb and ub.
Which release are you using? Which optimizer are you using?
Your task might be easier to express with Problem Based Optimization.
Do not use nonlinear constraints for those sum constraints: you only need linear constraints for those. It is just a nuisance to write out the matrices.
Susan
on 19 Apr 2019
Accepted Answer
Walter Roberson
on 19 Apr 2019
For any one particular scalar k and scalar m, you can express sum_{j} sum_{i} c(i,j,k,m) in range 0 to 1 as a linear constraint. The portion relevant to that k and m would be in the A matrix like
A(something,:) = [zeros(1, SOMETHING), ones(1, I*J), zeros(1,SOMETHINGELSE)];
b(something) = 1;
A(something+1,:) = [zeros(1, SOMETHING), -ones(1,I*J), zeros(1,SOMETHINGELSE)];
b(something) = 0;
You would have to walk this through K by M iterations, increasing the value of SOMETHING by I*J each time, and decreasing the value of SOMETHINGELSE by the same value.
An easier way of generating this would be something like:
blk = repmat({[ones(1, I*J); -ones(1, I*J)]}, 1, K*M);
A = blkdiag(blk{:});
b = zeros(size(A,1));
b(1:2:end) = 1;
21 Comments
Susan
on 19 Apr 2019
Walter Roberson
on 20 Apr 2019
x=c(:);
A*x<=b
Susan
on 20 Apr 2019
Walter Roberson
on 22 Apr 2019
Do not use a quoted string for the first argument of fmincon. Always pass it a function handle instead.
(By the time you know enough MATLAB to know when this rule can be safely violated, you will not want to violate it and will dislike that you have to violate it.)
[x, fval] = fmincon(@f, c0, A, b, [], [], lb, ub)
Walter Roberson
on 22 Apr 2019
I am lost as to what your f is. Above you defined syms c and the appear to assign to a particular cell array location in f based on indexing c, which was going to fail because syms c defines a scalar symbol and indexing a scalar symbol anywhere other than offset 1 will fail. But then you defined c as a matrix. Okay, but what is the definition of f now?
Susan
on 22 Apr 2019
Walter Roberson
on 22 Apr 2019
At the moment it is not obvious to me why you are using a cell array for f, instead of a sym array of size I J K M, such as
f = zeros(I, J, K, M, 'sym');
Your f is defined in terms of the symbolic array c, so your result of Calculatesumr() is going to be in terms of the variables in the symbolic array c because it involves f and f is defined in terms of the symbolic array c.
You define objfun in terms of a dummy numeric parameter c that will be ignored, and then Calculatesumr() will be called, returning an expression in terms of the symbolic variables c3_2_5_4, c2_1_4_3, and so on (what was in the symbolic array c.) fmincon() will then complain because the result is not numeric.
When you define a parameter named c to a function, and the function involves symbolic variables that were originally stored in a variable named c, then there is no connection made between the parameter and the symbolic variables -- not unless you deliberately subs() the parameters in.
What you should probably be doing is using matlabFunction() with the 'vars' parameter to convert the symbolic expression resulting from Calculatesumr into an anonymous function (taking numeric inputs) that can be called by fmincon()
Susan
on 23 Apr 2019
Walter Roberson
on 23 Apr 2019
Use
'vars', {reshape(c,1,[])}
instead of
'vars', c
in matlabFunction
Susan
on 23 Apr 2019
Walter Roberson
on 23 Apr 2019
What size is your c0 ?
fmincon reshapes the vector of values into the same shape as c0 before passing it in. If your c0 is a 2D array then 'vars', {c} should be fine.
Walter Roberson
on 23 Apr 2019
Yes, 'vars', {c} should work for that.
Susan
on 24 Apr 2019
More Answers (1)
Susan
on 22 Apr 2019
2 Comments
Walter Roberson
on 22 Apr 2019
Use the blkdiag() method I posted as "easier way of generating this". It generates the entire A and b matrix in a small number of lines.
Susan
on 22 Apr 2019
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