Why do I get an error using "-" along with the message "too many output arguments" when using fmincon?

Hello, I am using fmincon to optimize an objective function via a loop through different values of 2 specific parameters.

The optimization is done by defining a policy function. The policy function iteratively optimizes the objective function "fValue2".

"fValue2" has 2 output arguments viz. the objective function's value, and the gradient of the function.

My aim is to maximize the function. I attach an excerpt relevant to my specific problem below.

%Define policy function that will iteratively solve the optimization problem and return
%values of the choice variables and the corresponding optimized function
%value for each given value of 2 heterogeneity parameters

function [Choices, NPV] = fPolicyFunction(theta1, theta2, vector_eps, vector_p, ...
                                                       a, Delta, Gamma, m, beta, ,  ...
                                                                           points_p, points_eps, tau1, tau2, tau3)
%Define values of parameters that will be fixed throughout such as tau1,
%tau2, Delta etc, set NaN matrices for Choices and NPV etc..

% Set options for FMINCON
options = optimoptions('fmincon','Algorithm','interior-point','SpecifyObjectiveGradient',true, ...
    'HessianFcn', @hessianfcn,'Display','off','AlwaysHonorConstraints','bounds');

%Start Loop
for state_eps   = 1:points_eps
%     insert code which defines 'Upper Limit' as a function of state_eps
%     (omitted here for the sake of brevity)
    state_p = 1;        
    [Choices(:, state_p, state_eps), NPV(state_p, state_eps)] = fmincon(@(choices) -fValue2(state_p,  ...
                vector_p, state_eps, vector_eps, choices, parameters), StartChoices, [], [], [], [], LowerLimit, ...
                     UpperLimit, [], options);
end 
%End of Loop 

When I run the above code, I get the following error:-

Error using  - 
Too many output arguments.
Error in @(choices)-fValue2(state_p,vector_p,state_eps,vector_eps,choices,parameters)
Error in fmincon (line 577)
[initVals.f,initVals.g] = feval(funfcn{3},X,varargin{:});
Caused by:
Failure in initial objective function evaluation. FMINCON cannot continue.

My hunch is that the issue is being caused by the "-fValue2" section of the code. I use a "-" in front of the objective function since I wish to maximize. However, maybe the presence of the second output argument in fValue2 (i.e., its gradient) might be causing a problem? I couldn't figure out any other reason why this error might be showing up.

I would be grateful if anyone could help me in this regard. Happy to provide more clarification/explanations if required. Thank you!

Answer 1

[Matt J]

You have not shown us fValue2, but more than likely, it does not specify any output arguments to be returned.

[Vikramsinh]

Hello,

Thanks so much for your response. I attach below code pertaining to fValue2 for your reference.

function[NPVCashFlow,g] = fValue2(state_p,vector_p,state_eps,vector_eps,choices,parameters)

%insert code which defines parameter values for beta, delta, p, theta etc... 

%define NPV 
NPVCashFlow = -p .* Y - Phi - (KHigh + KLow) + beta .* ((fOutput(KHigh, a, theta1, epsilon) - ...
        TaxLiabilityHigh -  ShiftingCostHigh + (1 - Delta) .* KHigh) + ...
       (fOutput(KLow,  a, theta2, epsilon)  - TaxLiabilityLow  -  ShiftingCostLow  ...
       + (1 - Delta) .* KLow));

if nargout>1 %gradient required 

%Y_FOC 
Y_FOC = -p + ((beta.*m.*(ShiftingCostHigh.*TrueBaseHigh + ShiftingCostLow.*TrueBaseLow))./Y); 

%KHigh_FOC
KHigh_FOC = -1 + beta + beta.*(F_KHigh - Delta).*(1-TauHigh.*(1-AlphaHigh)-TauX.*AlphaHigh ...
    - ShiftingCostHigh - TrueBaseHigh.*CostBHigh); 

%KLow_FOC
KLow_FOC = -1 + beta + beta.*(F_KLow - Delta).*(1-TauLow.*(1-AlphaLow)-TauX.*AlphaLow - ...
              ShiftingCostLow - TrueBaseLow.*CostBLow); 

g = [KHigh_FOC;KLow_FOC;Y_FOC]' ; 
end

return 

[Matt J]

No idea. Show us how you're running the function.