symbolic matrices optimization with fmincon

Question

ali akbar 2020-10-2

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/603844-symbolic-matrices-optimization-with-fmincon

评论： ali akbar 2020-10-16

采纳的回答： Alan Weiss

在 MATLAB Online 中打开

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.

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Answer 1

Alan Weiss 2020-10-5

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/603844-symbolic-matrices-optimization-with-fmincon#answer_505303

在 MATLAB Online 中打开

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)