Why does MATLAB fmincon ignore non-linear constraints?

Question

I want to use MATLABs fmincon function to solve a non-linear problem of which I know that it can be solved in a different way very easily but I want to use fmincon (you might not need the following detailed information about the problem but I provided them in case you need):

Function f(x) is a quadratic function with its vertex at point (5|1).

f(x)=0.1(x-5)^2+1 for 0<=x<=5

Function g(x) is a polynom of order 4 with its vertex at Point (c|0).

g(x)=(x-c)^4 for 0<=x<=c

Function h is just a line on the x axis.

h=0 for c<=x<=5

I want to minimize the Area between the function f(x) and the two connected functions g(x) and h, in the interval [0,5]

minimize A=2*(int(f,[0,5])-int(g,[0,c]))=55/3 - (2*c^5)/5

Also I have the constraint that f(x) must always be 1 unit above the functions g(x) and h.

From the graph I know that the variable c must be between 0 and 2 (just a range for the fmincon function).

This is my .m file:

clc
clear

format long;
options = optimoptions(@fmincon, 'Display', 'iter', 'Algorithm', 'interior-point');

fun=@(x)55/3 - (2*(x(1))^5)/5;

lb = [0];
ub = [2];

[x,fval] = fmincon(fun,[0.1],[],[],[],[],lb,ub,@cons_Q6,options)

The constraints file looks like this (I inserted a lot of values for x with an increment of 0.1):

function [c,ceq]=cons_Q6(x)
c=[(0.0-x(1))^4-0.1*(0.0-5)^2
(0.1-x(1))^4-0.1*(0.1-5)^2
(0.2-x(1))^4-0.1*(0.2-5)^2
(0.3-x(1))^4-0.1*(0.3-5)^2
(0.4-x(1))^4-0.1*(0.4-5)^2
(0.5-x(1))^4-0.1*(0.5-5)^2
(0.6-x(1))^4-0.1*(0.6-5)^2
(0.7-x(1))^4-0.1*(0.7-5)^2
(0.8-x(1))^4-0.1*(0.8-5)^2
(0.9-x(1))^4-0.1*(0.9-5)^2
(1.0-x(1))^4-0.1*(1.0-5)^2
(1.1-x(1))^4-0.1*(1.1-5)^2
(1.2-x(1))^4-0.1*(1.2-5)^2
(1.3-x(1))^4-0.1*(1.3-5)^2
(1.4-x(1))^4-0.1*(1.4-5)^2
(1.5-x(1))^4-0.1*(1.5-5)^2
(1.6-x(1))^4-0.1*(1.6-5)^2
(1.7-x(1))^4-0.1*(1.7-5)^2
(1.8-x(1))^4-0.1*(1.8-5)^2
(1.9-x(1))^4-0.1*(1.9-5)^2
(2.0-x(1))^4-0.1*(2.0-5)^2
(2.1-x(1))^4-0.1*(2.1-5)^2
(2.2-x(1))^4-0.1*(2.2-5)^2
(2.3-x(1))^4-0.1*(2.3-5)^2
(2.4-x(1))^4-0.1*(2.4-5)^2
(2.5-x(1))^4-0.1*(2.5-5)^2
(2.6-x(1))^4-0.1*(2.6-5)^2
(2.7-x(1))^4-0.1*(2.7-5)^2
(2.8-x(1))^4-0.1*(2.8-5)^2
(2.9-x(1))^4-0.1*(2.9-5)^2
(3.0-x(1))^4-0.1*(3.0-5)^2
(3.1-x(1))^4-0.1*(3.1-5)^2
(3.2-x(1))^4-0.1*(3.2-5)^2
(3.3-x(1))^4-0.1*(3.3-5)^2
(3.4-x(1))^4-0.1*(3.4-5)^2
(3.5-x(1))^4-0.1*(3.5-5)^2
(3.6-x(1))^4-0.1*(3.6-5)^2
(3.7-x(1))^4-0.1*(3.7-5)^2
(3.8-x(1))^4-0.1*(3.8-5)^2
(3.9-x(1))^4-0.1*(3.9-5)^2
(4.0-x(1))^4-0.1*(4.0-5)^2
(4.1-x(1))^4-0.1*(4.1-5)^2
(4.2-x(1))^4-0.1*(4.2-5)^2
(4.3-x(1))^4-0.1*(4.3-5)^2
(4.4-x(1))^4-0.1*(4.4-5)^2
(4.5-x(1))^4-0.1*(4.5-5)^2
(4.6-x(1))^4-0.1*(4.6-5)^2
(4.7-x(1))^4-0.1*(4.7-5)^2
(4.8-x(1))^4-0.1*(4.8-5)^2
(4.9-x(1))^4-0.1*(4.9-5)^2
(5.0-x(1))^4-0.1*(5.0-5)^2
];
ceq=[];

As you can see, I've set the bounds for the unknown variable so that x(1)=[0,2] and I have set the constraints in the range [0,5] although I would only need them in the range of [0,2] because of the bounds for x(1). Now, when I solve it like this I get a solution that doesn't fit all the constraints. But when I delete the unneccessary constraints in the range ]2;5]

function [c,ceq]=cons_Q6(x)
c=[(0.0-x(1))^4-0.1*(0.0-5)^2
(0.1-x(1))^4-0.1*(0.1-5)^2
(0.2-x(1))^4-0.1*(0.2-5)^2
(0.3-x(1))^4-0.1*(0.3-5)^2
(0.4-x(1))^4-0.1*(0.4-5)^2
(0.5-x(1))^4-0.1*(0.5-5)^2
(0.6-x(1))^4-0.1*(0.6-5)^2
(0.7-x(1))^4-0.1*(0.7-5)^2
(0.8-x(1))^4-0.1*(0.8-5)^2
(0.9-x(1))^4-0.1*(0.9-5)^2
(1.0-x(1))^4-0.1*(1.0-5)^2
(1.1-x(1))^4-0.1*(1.1-5)^2
(1.2-x(1))^4-0.1*(1.2-5)^2
(1.3-x(1))^4-0.1*(1.3-5)^2
(1.4-x(1))^4-0.1*(1.4-5)^2
(1.5-x(1))^4-0.1*(1.5-5)^2
(1.6-x(1))^4-0.1*(1.6-5)^2
(1.7-x(1))^4-0.1*(1.7-5)^2
(1.8-x(1))^4-0.1*(1.8-5)^2
(1.9-x(1))^4-0.1*(1.9-5)^2
(2.0-x(1))^4-0.1*(2.0-5)^2
];
ceq=[];

then I get the right result. Does anyone know why this happens and why MATLAB does not respect the constraints when I put them up for the whole range [0,5]?

Why does MATLAB fmincon ignore non-linear constraints?

Answers (1)

Related Questions