fmincon with constraints on eigenvalues

Hello everybody, I need to perform an optimization on matlab, I'm using fminsearch, but I realized that I need to put some constraints on a part of the parameter vector.

my parameter vector size is 20*1, I need the matrix :

K= Vec2mat(param(1:9),3) to have eigenvalues with positive real parts.

I wrote: [param, ML] = fmincon(@(param) Myfct(param,maturity,Data),param0,[],[],[],[],[],[],@Myconstr, options)

with the function Myconstr being:

function [c,ceq] = Myconstr(x) c = -real(eig(vec2mat(x(1:9),3)))'; ceq=[]; end

but it doesn't seem to work. Appreciate any help.

Thanks

[Shashank Prasanna]

'but it doesn't seem to work' is not enough information. What is the error message? What is the expected output? What does Myfct look like?

[Ben]

Any thoughts ?

[Matt J]

My thought is that Shashank's questions above are worth answering.

Also, what is Vec2mat(a,b)? Is it the same as reshape(a,[],b) ?

[Ben]

Thanks Shashank for your reply, I didn't see your comment while posting my message. Here is my error msg:

??? Error using ==> eig Input to EIG must not contain NaN or Inf.

Error in ==> Myconstr at 3 c = -real(eig(vec2mat(x(1:9),3)))';

Error in ==> nlconst at 816 [nctmp,nceqtmp] = feval(confcn{3},x,varargin{:});

Error in ==> fmincon at 720 [X,FVAL,LAMBDA,EXITFLAG,OUTPUT,GRAD,HESSIAN]=...

Error in ==> Main at 22 [param, ML] = fmincon(@(param) KalmanFilterCorr(param,maturity,Data),param0,[],[],[],[],[],[],@Myconstr, options)

I'm trying to implement a model (an affine 3-factors IR model, the 3 factors are level slope and curvature), I did KalmanFilter+MLE to estimate the model parameters (K: mean reversion matrix, sigma: volatility matrix, theta: mean vector and lambda: decay)

Model : dXt = K(theta-Xt)*dt + sigma*dWt

where: Xt=(Lt, St, Ct)

my parameter vector contains the elements of the matrix K (9 elements) and theta (3) and the volatility matrix (6, inf triangular)

Matt, Vec2mat is there to convert a vector into a matrix, same as reshape

Thanks for your help.

[Matt J]

What does (6, inf triangular) mean? Do you mean that it is lower triangular?

Answer 1

[Matt J]

As Shashank said, we need to see KalmanFilterCorr to know what's going on, but it looks like you have reached values for params(1:9) that are not finite and therefore EIG complains.

Using the DBSTOP command ("dbstop if naninf") will force MATLAB to pause execution at the point in the code where nan/inf values for params are generated. Then you can see what's going on.