MATLAB: How to get the derivative of a complex function including reshape, max operation

chain rulederivativefmincongradientjacobianmaxminoptimizationreshape

I have a function name I want to optimize with to minimize this function
And I want to provide the gradient of function to speed up the optimization.
The definition of is 
function [F] = f(x)
    % size(x) = [a*b, 1]
    Z = reshape(x, [a, b]); % size(Z）= [a, b]
    % size(A) = [c, a]
    B = A * Z; % size(B) = [c, b]
    % size(C) = [c, b]
    D = sum(B.*C, 2); % [c, 1]

    E = abs(D).^2; % [c, 1]
    F = max(E); % scalar, my objective
end
I want to use chain rules, but I have the following questions:
  1. I cannot figure an easy way to get the jacobian of , i.e. the reshape function.
  2. the jacobian of
  3. the jacobian of function.
Thank you for your help!!

Best Answer

The Jacobian of B(x) is
J1=kron(speye(b),A);
The Jacobian of D(B) is,
J2=kron(ones(1,b),speye(c));
J2(logical(J2))=C;
The max(E) function is not differentiable everywhere, so it is not clear how well fmincon will handle this problem, but at the points where it is differentiable, the Jacobian is,
 N=length(E);
 e=zeros(1,N);
 
[~,idx]=max(E);
 e(idx)=1;
 
J3=spdiags(e(:),0,N,N);
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