Using pinv in optimproblem

I try to solve a constrained optimisation problem, where the variable is a vector. In one of the constraints I use pinv, but this creates an error code as this:

Error using svd
First input must be single or double.

Error in pinv (line 18)
[U,S,V] = svd(A,'econ');

Error in CAPM_2 (line 21)
cons2 = (w'*r*pinv(D)*(ones(n-1,1)-beta(1:(n-1)))==mu_M);

I cannot find a way around this (happy to use other optimisation routines)

My code:

r=0.05;         %exogenous parameters
mu_M=0.1;

n=2;            %dimension of vector

w=cumsum([1:n])';   %creating a vector of weights
w=w.^2;
w=w/sum(w);

prob = optimproblem('ObjectiveSense','min');
beta = optimvar('beta',n);
prob.Objective = (ones(n,1)-beta)'*(ones(n,1)-beta); %objective function is minimizing the norm over beta with the below constraints
cons1 = (w'*beta==1);
D=eye(n)-beta*w';   %This creates a matrix for the second constraint. It is singular (w'*ones(n,1)=1)
D=D(1:(n-1),:);     %Cuts the excess line out
cons2 = (w'*r*pinv(D)*(ones(n-1,1)-beta(1:(n-1)))==mu_M);
prob.Constraints.cons1 = cons1;
prob.Constraints.cons2 = cons2;

show(prob)

Answer 1

[Walter Roberson]

pinv() and matrix division are not supported.

However, for 1 x N variables, then

PINV_D = (D./sum(D.*conj(D))).'

[Andreas Krause]

Unfortunately, D in general has dimension n x (n-1), so this won't work, except in your special case

[Walter Roberson]

If your n does not change all that much, and if you have the Symbolic Toolbox, you could generate the general forms for the n you are likely to use, and use matlabFunction() to save them to files; do that ahead of time, and then at run-time pull out the appropriate function and invoke it on the optimization variable.

[Andreas Krause]

The n changes quite a bit (from 10 to about 5000), plus the w will be changing a lot (I just put an example in there I use for testing).

I can get an analytical expression for the first order condition of the minimum, which I then could use to solve, but this also involves pinv or inv.

[Walter Roberson]

Unfortunately your needs appear to be beyond the current capabilities of problem-based optimization; you might need to use solver-based optimization.

[Andreas Krause]

Thanks for your help. A shame it does not work this way. Off to solvers then...

[Matt J]

@Andreas Krause

For the problem you've shown, there would scarcely be an advantage to using the problem-based framework even if pinv were supported. You don't have any complicated linear constraints or a complicated partitioning of beta into sub-vectors.