MATLAB: Dealing with Error “Not enough Input Arguments” when using NONLCON for fmincon

fminconnon linear constraints

Hello,

I'm trying to solve a basic non linear programming problem. It involves 3 non linear inequality constraints. I'm just trying to write them in a function, but I keep getting the error "Not enough input arguments" in the function NONLCONhw6 whenever I try to run my full script. I'm very new to matlab, so I know it is probably something very simple but I am stumped. Also, I probably misused the terminology in this post and I apologize.

Here is my code:

function [c,ceq] = NONLCONhw6( x )
%UNTITLED3 Summary of this function goes here
%   Detailed explanation goes here
c(1) = x(1)^2 + x(2)^2 + x(3)^2 + x(4)^2 + x(1) - x(2) + x(3) - x(4) - 8;
c(2) = x(1)^2 + 2*x(2)^2 + x(3)^2 + 2*x(4)^2 - x(1) - x(4) - 10;
c(3) = 2*x(1)^2 + x(2)^2 + x(3)^2 + 2*x(1) - x(2) - x(4) - 5;
ceq = [];
end

Thank you!

Best Answer

Please show exactly how you run your script.

My speculation at the moment is that when you try to indicate the non-linear constraint function in the fmincon() call, that you are coding NONLCONhw6 instead of coding @NONLCONhw6

Related Solutions

MATLAB: Problems with fmincon, how to solve

Your problem is convex, so you can use the CVX package if you want. Also, the solution should be the global minimum; not a local minimum. To use fmincon, do the following:

Equality/nonEquality constraint:

function [c,ceq]=mycon(x)
c(1) = x(1)^2 + x(2)^2 - 4*x(1) - 3*x(2) + 5;
c(2) = -x(1)^2 - x(2)^2 + 4*x(1) + 3*x(2) - 6; % notice the fixed typo
ceq = 2*x(1)^2 + 2*x(2)^2 - 3*x(1) - 3*x(2) - 2; 
end

Construct the problem and call fmincon:

clc
clear all
Aeq=[]; 
beq=[]; 
A=[]; 
b=[]; 
% if you are not sure that vector x is within lb and ub do not restrict it
lb = []; %lb=[-3,-3]; 
ub = []; %ub=[3,3]; % 
x0=[4,4];
myObj = @(x) x(1)^2 + x(2)^2 - 5*x(1) - 6*x(2) + 15;
nonlcon = @mycon;
options = optimoptions('fmincon','Algorithm','sqp','Display','iter-detailed','MaxFunctionEvaluations',100000, 'MaxIterations',2000, 'OptimalityTolerance' ,1e-10);
[x,cost] = fmincon(myObj,x0,A,b,Aeq,beq,lb,ub,nonlcon)

Output (global minimum):


Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
<stopping criteria details>
x =
    1.6450    1.9007
cost =
    1.6896

MATLAB: Fmincon optimization with nonlinear constraint

nonlcon = @(x) deal([], x(1)-x(3)-(x(2)-x(4)))

However, you should consider rewriting with one fewer variable.

x(1)-x(3)=x(2)-x(4)

implies x(4) = x(2) + x(3) - x(1) .

Substituting in F=-(x(1)^2+x(2)^2+x(3)^2-x(4)^2) we get

F = -(x(1).^2 + x(2).^2 + x(3).^2 - (x(2) + x(3) - x(1)).^2)

This simplifies to

F = 2*(x2*x3 - x1*x3 - x1*x2)

and since this is an optimization task, the linear scale is not relevant, so you can use

F = x2*x3 - x1*x3 - x1*x2;

No non-linear constraint would be needed.

Best Answer

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MATLAB: Problems with fmincon, how to solve

MATLAB: Fmincon optimization with nonlinear constraint

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