MATLAB: How to minimize a nonlinear function f(x,y,z) over y and z subject to the constraint that y<=x ? Is it possible to get a minimum that depends on x

fmincon

How to minimize a nonlinear function f(x,y,z) over y and z subject to the constraint that y<=x ? Is it possible to get a minimum that depends on x ?

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xyz0 = sort(rand(1,3),'descend');     %starting point
A = [-1 1 0]; b = 0;
fmincon( @(xyz) f(xyz(1), xyz(2), xyz(3)), xyz0, A, b )

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MATLAB: 3D plotting of five inequalities

Hi Matthew. If you are looking for the portion of 3D space where points satisfy all the inequalities at the same time, then one way can be the following. Notice that I have just considered three of the inequalities you mentioned, but you can easily add them to the piece of code.

%define the range of x,y,z coordinates
step=.5;
x=-10:step:10;
y=-10:step:10;
z=-10:step:10;
%generate a grid with all triplets (x,y,z)
[X,Y,Z] = meshgrid(x,y,z);
%intersection of inequalities in a logical matrix
I = (X.*Y-X-Y+1>0) & (Z<1) & (X.*Y-X-Y-4*Z+1>0);
%plot of the points (x,y,z) that verify all inequalities
scatter3(X(I),Y(I),Z(I),'.');
xlabel('X'); ylabel('Y'); zlabel('Z');

Is this what you need? Max

MATLAB: Partition Domain Given Data of the Form w = f(x,y,z)

The function below exploits the fact that you can use the point u = [x,y,z] to calculate the partition location of the point. Once this is done, only partition containing points need processed. This converts the above problem from an O(n^3) problem to an O(n) problem. I have found that this method works really well for dividing data into partitions and finding the local mean in the partitions. This is about 10,000 times faster than the code listed above in my experience.

See File Exchange for code:

http://www.mathworks.com/matlabcentral/fileexchange/46970-partition-domain

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MATLAB: 3D plotting of five inequalities

MATLAB: Partition Domain Given Data of the Form w = f(x,y,z)

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