# How to plot 3D suraface and contour lines?

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ANCY S GEORGE on 2 Jun 2022
Answered: Bjorn Gustavsson on 2 Jun 2022
I want to plot the function
X0=[0;0];
lb=[-10;10];
ub=[-10;10];
f=@(x)(2*x(1)+20/x(1)+2*x(2)+20/x(2)+120);
x=fmincon(f,X0,[],[],[],[],lb,ub)
Initial point is a local minimum that satisfies the constraints. Optimization completed because at the initial point, 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.
x = 2×1
-10 10
How to plot the 3D surface and also the contour lines?

Bjorn Gustavsson on 2 Jun 2022
To effectively use matlab sometimes one has to make functions vectorized - such that you can feed the function arrays and get all results at once. This is such a case. Your f works well for the optimization. But if you define it this way:
f=@(x1,x2)(2*x1+20./x1+2*x2+20./x2+120);
You can still run it through fmincon:
X0=[1;1]; % Note that your function is undefined at [0, 0] due to the 2 1/x-terms
lb=[-10;-10]; % Note that I've changed the bounds. Yours constrained the solution to be
ub=[10;10]; % X1 = -10 and X2 = 10
x=fmincon(@(X) f(X(1),X(2)),X0,[],[],[],[],lb,ub);
and then effectively plot the function with surf and contour:
[x1,x2] = meshgrid(linspace(lb(1),ub(1),100),linspace(lb(2),ub(2),100));
hold on
contour(x1,x2,f(x1,x2),-200:30:400)
HTH

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