Optimization of complex variables in matlab

I am working with some optimization, I need to find the best $Lxp$ which is a control gain by minimizing the objective function $obj$ wich is the magnitude of the squares of the eigenvalues of phi_sol minus the values I enter $p1$ and $p2$. By programming in Matlab I have done this function.

function obj=objetivo(Lxp)%x,phi,gamma0,gamma1)
  global phi; %phi=[1 1;0 1]
  global gamma0; %  gamma0=[0.4900; 0.9900]
  global gamma1; %  gamma1=[0.0100; 0.0100]
  global p1
  global p2
  phi_sol= [1 0;0 1];
  for k=1:100
  phi_sol=phi+gamma0*Lxp+ gamma1*Lxp*inv(phi_sol);
  end
  E=vpa(eig(phi_sol))
  obj=abs((E(1)-p1)^2+(E(2)-p2)^2)

The optimization is done by using fminsearch so I do:

>>options = optimset('MaxFunEvals',10000,'TolFun',10^-11,'MaxIter',100000);
>>global p1; global p2; p1=0.7;p2=0.6;
>>[XOUT,FVAL,EXITFLAG]=fminsearch(@objetivo,[0.8 0.9],options)

It converges being $XOUT=[-0.1182 -0.6334]$ which is Lxp.

The problem comes when I need to find solution Lxp for complex $p1$ and $p2$, for example $p1=0.7+0.1*i$;$p2=0.6+0.05i$. My questions are: How should I work with complex variables in this particular optimization problem? How do I split them $p1$, $p2$ and E indeed, and calculate the objective function by using real and complex part?

[Matt J]

obj=abs((E(1)-p1)^2+(E(2)-p2)^2)

this looks like it should really be

 obj=norm(sort(E)-sort([p1;p2])).^2

Answer 1

[Matt J]

See here for the relevant technique

http://www.mathworks.com/matlabcentral/answers/102306-is-it-possible-to-use-the-fsolve-function-in-the-optimization-toolbox-to-solve-complex-equations

Also, I recommend you stop using global variables to pass fixed parameters to functions. There are better ways using anonymous and nested functions, discussed here

http://www.mathworks.com/help/optim/ug/passing-extra-parameters.html