Alternate way of defining given function using function handle for fmincon

I have an objective function which is of the form J = where C is a matrix of arbitrary constants which I have to determine along with 8 other arbitrary constants in the matrices A and B which appear in constraints and are known scalar matrices. I defined this objective function in MATLAB after evaluating the 4 product terms as follows-

fun =@(x) (x(9)+x(10)+x(11))^2+(x(9)+x(10)-x(11))^2+(x(9)-x(10)+x(12))^2+(x(9)-x(10)-x(12))^2;

where x(9) to x(12) are the 4 arbitrary constants in the matrix C and x(1) to x(8) are the 8 arbitrary constatnts in the matrices A and B. Then after setting

x0 = zeros(1,12);

and writing the constraints in terms of x(1) to x(8), I got all the 12 arbitrary constants x(1) to x(12) using fmincon. Now what I want is to write this objective function without evaluating each term. Is there any way to do the same?

[Saurabh Madankar]

One other way I could define this function is

fun =@(x) ([x(9) x(10) x(11) x(12)]*h(1))^2 + ([x(9) x(10) x(11) x(12)]*h(2))^2 + ...
    ([x(9) x(10) x(11) x(12)]*h(3))^2 + ([x(9) x(10) x(11) x(12)]*h(4))^2;

Is there any other way of writing the following row vector?

[x(9) x(10) x(11) x(12)]

[Saurabh Madankar]

I further reduced this as

fun =@(x) ([x(9:12)]*h(1))^2 + ([x(9:12)]*h(2))^2 + ([x(9:12)]*h(3))^2 + ([x(9:12)]*h(4))^2;

Now only thing thats remaining is instead of writing these four terms, how can I write this as summation of a single term?

Answer 1

[Matt J]

Gather the into a 4x4 matrix H and A,B,C into an unknown 4x3 matrix X. Then write the problem as,

%X=[A,B,C]   
%H=[h1,h2,h3,h4]

fun=@(X) norm(X(:,3).'*H).^2;

X0=zeros(4,3);

fmincon(fun,X0,Aineq,bineq,Aeq,beq,lb,ub,@nonlcon,opts)

function [c,ceq]=nonlcon(X)

  A=X(:,1); B=X(:,2); C=X(:,3); %unpack
   
 c=_____
 ceq=_____
end

[Saurabh Madankar]

Thanks a lot, this works.