fmincon "not enough input argument"

I'm trying to optimize a nested objective function. The main script is as follows:

c = 1;
cd data;
formatSpec = 'c_p_%d.csv';
filename = sprintf(formatSpec,c);
data = readtable(filename, 'ReadVariableNames', true);
cd ..

alphaGuess = 0.01;
rhoGuess = 0.01;
beta_bGuess = 0.5;
beta_sGuess = 0.5;
beta_nGuess = 0.5;

A = [0 0 -1 1 0; 0 0 0 -1 1];
b = [0; 0];
Aeq = [];
beq = [];
lb = [0 0 0 0 0];
ub = [1 1 1 1 1];

x0 = [alphaGuess rhoGuess beta_bGuess beta_sGuess beta_nGuess];

x = fmincon(L_c,x0,A,b,Aeq,beq,lb,ub);

alpha = x(1);
rho = x(2);
beta_b = x(3);
beta_s = x(4);
beta_n = x(5);

The objective function L_c is defined in the following file:

function L = L_c(alpha,rho,beta_b,beta_s,beta_n)
    data = readtable('data');
    N = length(data.id);
    P_vector = zeros(N,1);
    for i = 1:N
        k = string(data.k(i));
        theta_b = data.b_prod(i);
        theta_s = data.s_prod(i);
        P_vector(i) = log(P_i(alpha,rho,theta_b,theta_s,beta_b, beta_s,beta_n,k));
    end
    P_vector(isnan(P_vector))=0;
    L = - sum(P_vector);
end

P_i, the function in L_c, is defined in another file:

function P = P_i(alpha,rho,theta_b,theta_s,beta_b,beta_s,beta_n,k)
    beta = beta_b;
    Psi_b = Psi_i_k(alpha,rho,theta_b,theta_s,beta);
    beta=beta_s;
    Psi_s = Psi_i_k(alpha,rho,theta_b,theta_s,beta);
    beta=beta_n;
    Psi_n = Psi_i_k(alpha,rho,theta_b,theta_s,beta);
    if string(k) == 'b'
        P = exp(Psi_b)/(exp(Psi_b)+exp(Psi_s)+exp(Psi_n));
    elseif string(k) == 's'
        P = exp(Psi_s)/(exp(Psi_b)+exp(Psi_s)+exp(Psi_n));
    else
        P = exp(Psi_n)/(exp(Psi_b)+exp(Psi_s)+exp(Psi_n));
    end
end

Psi_i_k, the function inside P_i, is defined in another file:

function Psi = Psi_i_k(alpha,rho,theta_b,theta_s,beta)
    Alpha = alpha.^(alpha/(1-alpha));
    Buyer = (theta_b*beta).^(rho/(1-rho));
    Seller = (theta_s*(1-beta)).^(rho/(1-rho));
    Numerator = (1-alpha*beta)*Buyer + (1-alpha*(1-beta))*Seller;
    Denominator = (Buyer+Seller).^((rho-alpha)/(rho*(1-alpha)));
    Psi=Alpha*Numerator/Denominator;
end

When I run the main script without fmincon, Matlab returns a valid value. But when I run the fmincon function, Matlab returns the following error message:

I have attached a replication file to this post. Could someone please help me figure out what is wrong? Thanks!

Answer 1

[Alan Weiss]

What are your control variables? I mean, the variables that you want fmincon to move to look for an optimum? It looks like you want alpha,rho,beta_b,beta_s,beta_n to be the control variables.

If this is the case, then you need to make a new variable x = [alpha,rho,beta_b,beta_s,beta_n] and write L_c in terms of x:

function L = L_c(x)
alpha = x(1);
rho = x(2);
beta_b = x(3);
beta_s = x(4);
beta_n = x(5);
... % I mean the rest of your code goes here

Then you need to call the function differently:

x = fmincon(@L_c,x0,A,b,Aeq,beq,lb,ub); % Notice the @

See Writing Scalar Objective Fucntions.

Alan Weiss

MATLAB mathematical toolbox documentation

[Xiaoji Xu]

Thanks for your response! My control variables are (alpha, rho, beta_b, beta_s, beta_n). I use fmincon to solve a log-likelihood maximization problem. I corrected the code as per your suggestion. Now the main script looks like this:

close all
clear
clc

c = 1;
cd data;
formatSpec = 'c_p_%d.csv';
filename = sprintf(formatSpec,c);
data = readtable(filename, 'ReadVariableNames', true);
cd ..

alphaGuess = 0.01;
rhoGuess = 0.01;
beta_bGuess = 0.5;
beta_sGuess = 0.5;
beta_nGuess = 0.5;

A = [0 0 -1 1 0; 0 0 0 -1 1];
b = [0; 0];
Aeq = [];
beq = [];
lb = [0 0 0 0 0];
ub = [1 1 1 1 1];

x0 = [alphaGuess rhoGuess beta_bGuess beta_sGuess beta_nGuess];

x = [alpha,rho,beta_b,beta_s,beta_n];

x = fmincon(@L_c,x0,A,b,Aeq,beq,lb,ub);

The L_c function in a separate file looks like this:

function L = L_c(x)
    alpha = x(1);
    rho = x(2);
    beta_b = x(3);
    beta_s = x(4);
    beta_n = x(5);
    data = readtable('data');
    N = length(data.id);
    P_vector = zeros(N,1);
    for i = 1:N
        k = string(data.k(i));
        theta_b = data.b_prod(i);
        theta_s = data.s_prod(i);
        P_vector(i) = log(P_i(alpha,rho,theta_b,theta_s,beta_b, beta_s,beta_n,k));
    end
    P_vector(isnan(P_vector))=0;
    L = - sum(P_vector);
end
When running the main script, however, I encounter the following error message:

[Alan Weiss]

Get rid of the line causing the error:

x = [alpha,rho,beta_b,beta_s,beta_n];

This line does nothing but throw an error. If you want to keep it as a reminder, comment it out.

Alan Weiss

MATLAB mathematical toolbox documentation

[Xiaoji Xu]

It worked. Thanks!