Multiple linear equality constraints in fmincon

Hi

I am optimising the elements of a matrix X based on an ojbective function. I know what value of sum of row elements and sum of column elements should be. I want to optimize the matrix based on these 2 constraints.

If the size of the matrix is , for row and column,

1) sum of column 1 elements: = known column 1 sum.

This can be done for every column giving n column constraints.

I can represent this in

where =ones(1,n) and = known vector

2) I need to do the same for row elements too. I have the known vector.

I'm unable to define one and which constraints the row sum as well as column sum of matrix X

Thank you

Answer 1

[Torsten]

Aeq = [1 0 1 0 ; 0 1 0 1 ; 1 1 0 0 ; 0 0 1 1];
beq = [sum of column 1 ; sum of column 2 ; sum of row 1 ; sum of row 2]
X = [X11 ; X12 ; X21 ; X22]

This is the configuration for n=2. Can you take it from here ?

[sharadhi]

Yes. That was something I didn't think of. Thanks Torsten