How do I address "Error using barrier (line 31) Gradient at initial point contains Inf, NaN, or complex values. Fmincon cannot continue."

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J. Womack 2015-8-10

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https://ww2.mathworks.cn/matlabcentral/answers/233140-how-do-i-address-error-using-barrier-line-31-gradient-at-initial-point-contains-inf-nan-or-comp

评论： Walter Roberson 2015-8-15

I have created an output function that I am using with fmincon that provides a gradient as an output. When optimizing, I keep getting the following error:

----------------------------------------------

Error using barrier (line 31)
Gradient at initial point contains Inf, NaN, or complex values. Fmincon cannot continue.
Error in fmincon (line 799)
    [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...
Error in loop_gradtest>(parfor body) (line 13)
wts_out(:,i) = fmincon(@(x)utility_gradtest(x,score_param1,
score_param2,rets),x,[],[],[mean(returns_grid_parallel)*12;ones(1,size(returns_grid_parallel,2))],[.05;1],double(limits_min(:,2)),double(limits_max(:,2)),[],fmin_options);
Error in loop_gradtest (line 9)
parfor i=1:10000;

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The function gradtest is used to all another function, utility_gradtest that is used to calculate maximum (min negative) utility given a vector of weights. In this function, using finite differencing, I calculate a gradient that is then supplied as part of the output for utility_gradtest.

I've used the following input in setting my options:

fmin_options = optimset('Algorithm','interior-point','GradObj','on','MaxFunEvals',10000,'MaxIter',500,'TolCon',10e-16,'TolX',10e-16,'Display','off','UseParallel',true);

Do I need to incorporate error handling capability to account for when the gradient contains an undefined point?

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J. Womack 2015-8-14

在 MATLAB Online 中打开

Thank you both for your responses.

My gradient function is the following:

function [gradient] = utility_gradient(x,score_param1, score_param2,returns_grid_parallel)
    %Set values for parameters
    a = score_param2; %loss aversion parameter
    p = score_param1; %risk aversion parameter
    port_annual_return = (mean(returns_grid_parallel).*12)'.*x;
    port_annual_std = (cov(returns_grid_parallel).*12)*x./sqrt(x'*(cov(returns_grid_parallel).*12)*x);
es_low_z = -(1./sqrt(2*pi).*exp(-((0-(mean(returns_grid_parallel).*12)'.*x)./((cov(returns_grid_parallel).*12)*x./sqrt(x'*(cov(returns_grid_parallel).*12)*x))).^2./2))./ ...
              (.5*(erf(((0-(mean(returns_grid_parallel).*12)'.*x)./((cov(returns_grid_parallel).*12)*x./sqrt(x'*(cov(returns_grid_parallel).*12)*x)))./sqrt(2))+1));
  es_high_z = (1./sqrt(2*pi).*exp(-((0-(mean(returns_grid_parallel).*12)'.*x)./((cov(returns_grid_parallel).*12)*x./sqrt(x'*(cov(returns_grid_parallel).*12)*x))).^2./2))./ ...
               (1-.5*(erf(((0-(mean(returns_grid_parallel).*12)'.*x)./((cov(returns_grid_parallel).*12)*x./sqrt(x'*(cov(returns_grid_parallel).*12)*x)))./sqrt(2))+1));                                                                          
    gradient = -a.*(.5*(erf(((0-(mean(returns_grid_parallel).*12)'.*x)./((cov(returns_grid_parallel).*12)*x./sqrt(x'*(cov(returns_grid_parallel).*12)*x)))./sqrt(2))+1)).*exp(-p.*(1+port_annual_return+es_low_z.*port_annual_std))+ ...
                -(1-(.5*(erf(((0-(mean(returns_grid_parallel).*12)'.*x)./((cov(returns_grid_parallel).*12)*x./sqrt(x'*(cov(returns_grid_parallel).*12)*x)))./sqrt(2))+1))).*exp(-p.*(1+port_annual_return+es_high_z.*port_annual_std));
    end

The function itself just calculates a scalar value for a utility function; I use the current weight vector, then add a tiny increment, and calculate the gradient numerically. (When I clean up the flow for production, I will eliminate running the same function twice as can be seen below). The code to calculate the scalar function is below:

    function [utility_values,grad] = utility_gradtest(x,score_param1, score_param2,returns_grid_parallel)                              
%Set values for parameters
a = score_param2; %loss aversion parameter
p = score_param1; %risk aversion parameter
port_annual_return = mean(returns_grid_parallel*x).*12;
port_annual_std = std(returns_grid_parallel*x).*sqrt(12);
p_low = normcdf((0-port_annual_return)./port_annual_std,0,1);
es_low_z = -normpdf((0-port_annual_return)./port_annual_std,0,1)./p_low;
es_high_z =pdf(9)-normpdf((0-port_annual_return)./port_annual_std,0,1))./(1-p_low);
utility_values = mean(-(-a.*p_low.*exp(-p.*(1+port_annual_return+es_low_z.*port_annual_std))+ ...
-(1-p_low).*exp(-p.*(1+port_annual_return+es_high_z.*port_annual_std))));
grad = utility_gradient(x+repmat(.0000001,size(x)),score_param1, score_param2,returns_grid_parallel)- ...
                                         utility_gradient(x,score_param1, score_param2,returns_grid_parallel);
end

My initial value for the weight vector (x input) is a vector that represents equal weights:

repmat(1/n,n,1)

I am going to work on debugging but want to make sure my function isn't bombing out when things change.

Any thoughts you can share on either error handling or approach are greatly appreciated!

J. Womack 2015-8-14

Walter - thank you for the recommendation. I followed your advice and just focused on capturing the gradient from the parfor loop and found the problem. I've added in code to address NaNs and Infs and it's working.

I will run through the code and clean it up to try to capture additional speed and appreciate you pointing out the repetition. Where it's within the same function, I can make the change.

Thank you again for your help!