Allocation Optimization problem - Arrow Debreu

Hi,

Is it possible to optimize not only a single number but an entire matrix? here is a smaller scale version of my problem.

As you can see my matrix of x's is a kinda Arrow Debreu Asset matrix, where every x can only be used once in our matrix. I don't think I can do this with the intlinprog function or fmincon.

Thank you.

[Alexi]

Hi, did you solve this problem by fmincon? Thanks.

[KSSV]

Are you looking for something like this?

k = 10:10:70 ;
l = [1 0 0 1 1 0 0; 0 1 1 0 0 0 0;0 0 0 0 0 1 1] ;
K = repmat(k,size(l,1),1) ;
lhs = K.*l

Question is not clear.

Answer 1

[Walter Roberson]

This case appears to have multiple objectives, some of which could get worse if you made others better. You would probably need to do a multiobjective optimization.

One form of multiobjective is shown at https://www.mathworks.com/help/optim/ug/generate-and-plot-a-pareto-front.html which uses fgoalobtain to do pareto optimization.

You can also use gamultiobj to do pareto optimization.