How do I minimize a function graphically?

I am trying to minimize f (x1, x2) = (x1 − 1)^2 + (x2 − 5)^2

subject to

−x1^2 + x2 ≤ 4

−(x1 − 2)^2 + x2 ≤ 3

My MATLAB code is below:

clc

clear all

%

x = -0:10;

g1 = -x(1)^2+x(2)-4;

g2 = -(x(1)-2)^2+x(2)-3;

optim = (x(1)-1)^2+(x(2)-5)^2;

%

xlim([0 10])

ylim([0 10])

%

plot(x,g1,x,g2,x,optim,'--')

grid on

grid minor

xlabel('x')

ylabel('y')

Answer 1

[Sulaymon Eshkabilov]

In your code, your variables are x1 and x2 and NOT x. Moreover, g1 and g2 are incorrectly defined.

In this exercise, you should use fmincon() fcn of Optimization toolbox. See this doc: https://www.mathworks.com/help/optim/ug/minimization-with-bound-constraints-and-banded-preconditioner.html