How do I include a user specified hessian function for fmincon?

I am working on an optimisation code and I have a Hessian function I wish fmincon to use. I'm currently having trouble trying to get the correct command to include the Hessian. I am currently using:

options = optimoptions('fmincon','SpecifyObjectiveGradient',true,'HessFcn','objective','Display','iter','OutputFcn',@outfun);

For which I get the following error:

> In Temperature_inverse_problem (line 51)

Error using feval

Undefined function or variable 'objective'.

Error in computeHessian

Error in barrier

Error in fmincon (line 813)

[X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] =

barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...

Error in Temperature_inverse_problem (line 53)

X=fmincon(t_fun,X_old,A,b,Aeq,beq,LB,UB,[],options);

The code for my objective function is:

function [Y,G,H] = Boundary_temperature(T_data,t,R,X,Joule)
%UNTITLED5 Summary of this function goes here
%   Detailed explanation goes here
diff=battery_temp(t,R,X,Joule)-T_data;
integrand=0.5*(diff.^2);
Y=trapz(t,integrand);
G=grad_F(T_data,t,R,X,Joule);
Temp=cylinder_temp(t,R,X,Joule);
T=Temp(:,end);
T_theta=theta_grad(t,R,X,Joule);
T_kappa=kappa_grad(t,R,X,Joule);
T_hop=h_grad(t,R,X,Joule);
T_t=T_theta(:,end);
T_k=T_kappa(:,end);
T_h=T_hop(:,end);
H=Hessian_F(T_data,t,R,X,Joule,T,T_t,T_k,T_h);
end

Here Y is the objective function, G is the gradient and H is the Hessian. I've trolled the internet and I've not found anything which works. What am I doing wrong?

[Ameer Hamza]

How is t_fun defined in the call to fmincon.

Answer 1

[Alan Weiss]

If you read the documentation for Including Gradients and Hessians, you will see that the fmincon 'interior-point' algorithm does not allow you to use 'HessFcn'='objective'. Instead, you must write a Hessian function that is the Hessian of the Lagrangian. See Hessian for fmincon interior-point algorithm.

Alan Weiss

MATLAB mathematical toolbox documentation

[Matthew Hunt]

The documentation for matlab typically is a mess for things like this. Some of it is out of date and you have to see other people's code to figure out what to do.

I have since found some code which works.

[Alan Weiss]

I try very hard to keep the documentation clear, correct, and concise. If you ever find anything incorrect or unclear, please let me know either by emailing me directly or filing a bug report (we consider documentation errors to be bugs).

Alan Weiss

MATLAB mathematical toolbox documentation