symbolic matrices optimization with fmincon
2 views (last 30 days)
Show older comments
I am trying to minimize a function. The function is
, where
and
are defined as
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/370048/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/370051/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/370054/image.png)
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.
0 Comments
Accepted Answer
Alan Weiss
on 5 Oct 2020
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
More Answers (0)
See Also
Categories
Find more on Get Started with Optimization Toolbox in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!