MATLAB: Optimization problem: matlab inbuilt function “getIpOptions” generates an error in fmincon

Question

This code is used to generated the minimum quantities of two good given a cost constraints. it is a simple optimization problem using "fmincon", however when i run the code i get this problem

%{ 
Unrecognized function or variable 'getIpOptions'.
Error in fmincon (line 822)
    options = getIpOptions(options,sizes.nVar,mEq,flags.constr,defaultopt,10,0.01);
Error in langrangian (line 5)
[x,fval] = fmincon(@volume,[1 1],[],[],[],[],[0 0],[],@mycons);
%}

clear ;
clc;
close all;
[x,fval] = fmincon(@utility,[1 1],[],[],[],[],[0 0],[], @mycons);
% the utility function to be maximimzed
function u = utility(x)
    u = x(1)^(1/3)*x(2)^(2/3);
end
% subject to the cost function below
function s = cost(x)
    s = 10*x(1) + 4*x(2);
end
function[c,ceq] = mycons(x)
    c = cost(x) - 100 ; % the cost function is less than 100 (equality constraint)
    ceq = [] ; % we dont have non-linear equality constraints
end

Answer 1

You are trying to maximize utility, so you should minimize the negative of the utility. The following code runs without error for me:

[x,fval] = fmincon(@utility,[1 1],[],[],[],[],[0 0],[], @mycons)
% the utility function to be maximimzed
function u = utility(x)
    u = x(1)^(1/3)*x(2)^(2/3);
    u = -u;
end
% subject to the cost function below
function s = cost(x)
    s = 10*x(1) + 4*x(2);
end
function[c,ceq] = mycons(x)
    c = cost(x) - 100 ; % the cost function is less than 100 (equality constraint)
    ceq = [] ; % we dont have non-linear equality constraints
end

Alan Weiss

MATLAB mathematical toolbox documentation