The best way to code this optimization problem

I have a large optimization problem (a small part of this problem is given below)

max

s.t

Note that I have equality constraints

I need to code this in Matlab in an eficient way for a large-scale problem

[Hank]

Can you share what you've tried?

[mohamed Faraj]

I have not coded it yet. I just need a general advice on how to code it. Should I make a mapping from (b,l,n) to a one index variable r_k for example. For example, r_k, k=1,2,......24 or I better use the indexes (b,l,n). I prefer to use the three indexes as my problem is large and it is easier to track if I use the three indexes (b,l,n)

Answer 1

[Matt J]

It should be very straightforward using the problem-based solvers in the Optimization Toolbox,

https://www.mathworks.com/help/optim/ug/problem-based-workflow.html

[mohamed Faraj]

I have matlab 2013b

Answer 2

[Matt J]

I have matlab 2013b

Because the array sizes are fairly small here, the easiest thing might be to use my func2mat submission to express all your summations as matrix multiplications.

https://www.mathworks.com/matlabcentral/fileexchange/44669-func2mat-convert-linear-function-to-matrix

For example, a summation of a 4x1x12x12 array along its 3rd dimension can be represented by a matrix A obtained as follows,

z0=rand(4,1,12,12);
A=func2mat(@(z)sum(z,3) , z0);

To convince yourself of the equivalence, you can do

calc1=sum(z0,3);

calc2=A*z0(:);

>> norm(calc2(:)-calc1(:))     

ans =

     0