MATLAB: Symbolic matrices optimization with fmincon

error while optimizing with fminconfminconmatricesoptimizationsymbolic variable optimization

I am trying to minimize a function. The function is , where and are defined as
chi= rand(4,4) %% for example
syms t [1 16] real
tt=[t1 0 0 0;t5+1i*t6 t2 0 0;t11+1i*t12 t7+1i*t8 t3 0;t15+1i*t16 t13+1i*t14 t9+1i*t10 t4];
tt2=[t1 0 0 0;t5-1i*t6 t2 0 0;t11-1i*t12 t7-1i*t8 t3 0;t15-1i*t16 t13-1i*t14 t9-1i*t10 t4];
chi1=simplify(transpose(tt2)*tt) %% chi1 is 4x4 matrix with 16 symbolic variables
fun=sum((chi1-chi).^2);
g=matlabFunction(fun);
rng default;
gs=GlobalSearch;
opts=optimoptions(@fmincon,'Algorithm','interior-point');
problem = createOptimProblem('fmincon','x0',[],'objective',g,'lb',[],'ub',[],'options',opts)
t=run(gs,problem)
and I am encountering an incessant error
PROBLEM structure should have a non-empty X0 field.
After putting arbitrary values of 'x0' (16 values), the error changes to
not enough input arguments.
Currently, not able to sort out where the problem is. Any help will be appreciated.

Best Answer

  • I was able to modify your program to run. I don't know if it is correct, but at least it runs.
    chi= rand(4,4) %% for example
    syms t [1 16] real
    t = reshape(t,4,4); % You need this for the function to be well-defined
    tt=[t1 0 0 0;t5+1i*t6 t2 0 0;t11+1i*t12 t7+1i*t8 t3 0;t15+1i*t16 t13+1i*t14 t9+1i*t10 t4];
    tt2=[t1 0 0 0;t5-1i*t6 t2 0 0;t11-1i*t12 t7-1i*t8 t3 0;t15-1i*t16 t13-1i*t14 t9-1i*t10 t4];
    chi1=simplify(transpose(tt2)*tt) %% chi1 is 4x4 matrix with 16 symbolic variables
    fun=real(sum((chi1-chi).^2,'all')); % I had to take the real part because fmincon needs real values
    g=matlabFunction(fun,'vars',{t}); % This is also necessary: fmincon takes just one input argument
    rng default;
    gs=GlobalSearch;
    opts=optimoptions(@fmincon,'Algorithm','interior-point');
    problem = createOptimProblem('fmincon','x0',randn(4),'objective',g,'lb',[],'ub',[],'options',opts)
    t=run(gs,problem)
    Alan Weiss
    MATLAB mathematical toolbox documentation