Gradient Problem : FMINUNC requires two input arguments.

Hello, I have a problem with an optimization problem: When I try to perform the code, it gives the error:

Error using fminunc (line 168)
FMINUNC requires two input arguments.

Error in JournalReplicationUnconstrained_rt_xt_mlf2 (line 8)
opts = optimset(fminunc, 'GradObj','on','Algorithm','trust-region');

dataX = xlsread('Xt_dividends_trial3(ln)');
dataM = xlsread('Mt_performance_Variable');
dataR = xlsread('Rt_log_returns');
d_VW = dataX(:,2); % Dividend yields for Value weighted index
MVW = dataM(:,2); % performance variable for Value weighted index
RVW = dataR(:,2); % log returns for Value weighted index
N = length(dataX); dt = 1;
opts = optimset(fminunc, 'GradObj','on','Algorithm','trust-region');
objfun = @(theta) mlf4(theta, RVW, MVW, d_VW, N, dt);
theta0 = [-.0577;.0135;.0524; .011; .0092; .016; .15];
[theta, fv] = fminunc(objfun, theta0, opts)

By the way I need to keep theta0 unchanged.

Function:

function f = mlf4(theta, RVW, MVW, d_VW, N, dt)
sigmaX1 = theta(1);
sigmaX2 = theta(2);
sigmaS1 = theta(3);
alpha = theta(4);
mu0 =  theta(5);
mu1 = theta(6);
phi = theta(7);
%K = [sigmaS1^2, sigmaS1*sigmaX1*mu1; ...
    %sigmaS1*sigmaX1*mu1, ((sigmaX1 + sigmaX2)*mu1)^2];
f0 = N*0.5*log((2*pi)^2*mu1^2*sigmaS1^2*sigmaX2^2 + 2*sigmaX1*mu1^2*sigmaS1^2*sigmaX2);
f1 = 0;
for j = 2:N
    A = [RVW(j) - ((1-phi)*(mu0+mu1*d_VW(j-1))+phi*MVW(j-1))*dt; ...
        mu1*(d_VW(j)-d_VW(j-1)*(1-alpha*dt))];
    f1 = f1 + 0.5*A'*[(sigmaX1 + sigmaX2)^2/(sigmaS1^2*sigmaX2^2 + 2*sigmaX1*sigmaS1^2*sigmaX2), ...
        -sigmaX1/(mu1*sigmaS1*sigmaX2^2 + 2*mu1*sigmaS1*sigmaX1*sigmaX2); ...
        -sigmaX1/(mu1*sigmaS1*sigmaX2^2 + 2*mu1*sigmaS1*sigmaX1*sigmaX2), ...
        1/(mu1^2*sigmaX2^2 + 2*sigmaX1*mu1^2*sigmaX2)]*A;
end
f = f0+f1;
end

Thanks in advance.

Answer 1

[Torsten]

Use

options = optimoptions('fminunc','GradObj','on','Algorithm','trust-region');
theta0 = [-.0577, .0135, .0524,  .011, .0092, .016, .15];

and supply the gradient in mlf4.

Best wishes

Torsten.

[Armagan Ozbilge]

Hello,

Thank you for your help. However, what do you mean by supplying the gradient in mlf4? Like,

function [f, fGrad] = mlf4(theta, RVW, MVW, d_VW, N, dt)
.
.
.
fGrad = jacobian(f, theta);
or something else? If so, how can I put this gradient into fminunc?

Thanks in advance.

[Torsten]

Take a look at the example under

http://de.mathworks.com/help/optim/ug/fminunc.html

Best wishes

Torsten.