Adding feasible region on a Contour plot

Hi,

I am trying to plot a contour of an optimization problem and also determine the feasible region for the function.

I have been able to generate the contout plot but I I don't know how to plot the feasible region when the constraint is X > 0.

Example of my code is shown below.

Assuming the constraints is given by:

.

Thank you for your help

x = -5:0.005:5;
y = -5:0.005:5;
[X,Y] = meshgrid(x,y);
F = (X.^2+Y-11).^2 + (X + Y.^2 - 7).^2;
v = [0:2:10 10:10:100 100:20:200]
[c,h]=contour(X,Y,F,v,'linewidth',2);

[DGM]

It depends how you want to represent it. Do you want the whole plot from -5:5 with some sort of lines or mask to delineate the feasible region, or do you just want to plot the feasibile region alone?

[Telema Harry]

Thank you for the response. I want to plot only the feasible region.

I have mananced to plot the constraint line.. but it is not starting and ending at the point I want.

In the attached diagram, I have shaded the feasible region.

My other challenge is how to plot the straigth lines when

Answer 1

[DGM]

Like I mentioned, it depends how you want to represent the region. Let's say you want to represent the feasibility region within the context of the function over its entire domain. I suspect this, since you're solving for F over x,y=[-5 5], even though your constraints exclude negative inputs. There are probably a lot of things you could do. You could delineate the area with boundary lines, or you could de-emphasize the overall function representation using a masking approach. Let me just try something as an example:

clf
x = -5:0.05:5;
y = -5:0.05:5;
[X,Y] = meshgrid(x,y);
F = (X.^2+Y-11).^2 + (X + Y.^2 - 7).^2;
v = [0:2:10 10:10:100 100:20:200]

% plot the whole thing
[c,h]=contour(X,Y,F,v,'linewidth',2); hold on; axis equal
% but subdue it with an overlay
hf=fill([1 1 -1 -1]*5,[-1 1 1 -1]*5,'w','facealpha',0.8);

% plot just the ROI
feasible = (X>=0) & (Y>=0) & (X+2*Y<=2);
F(~feasible) = NaN;
contour(X,Y,F,v,'linewidth',2);

% maybe include lines if you want?
line([5 -5],[-1.5 3.5],'linestyle','--','color','k');
line([0 0],[-5 5],'linestyle','--','color','k');
line([-5 5],[0 0],'linestyle','--','color','k');

Alternatively, maybe you could find some way to represent the set of constraints using overlays (though maybe these colors are a big garish)

x = -5:0.005:5;
y = -5:0.005:5;
[X,Y] = meshgrid(x,y);
F = (X.^2+Y-11).^2 + (X + Y.^2 - 7).^2;
v = [0:2:10 10:10:100 100:20:200]

% plot the whole thing
[c,h]=contour(X,Y,F,v,'linewidth',2); hold on; axis equal
% do something to represent the constraint areas individually
hf1=fill([-1 0 0 -1]*5,[1 1 -1 -1]*5,[1 0.5 1],'facealpha',0.6,'edgecolor','none')
hf2=fill([1 1 -1 -1]*5,[-1 0 0 -1]*5,[0.5 1 1],'facealpha',0.6,'edgecolor','none')
hf3=fill([5 -5 -5 5 5],[-1.5 3.5 5 5 -1.5],[1 1 0.5],'facealpha',0.6,'edgecolor','none')

On the other hand, maybe you want to just plot the ROI by itself.

x = 0:0.005:2;
y = 0:0.005:1;
[X,Y] = meshgrid(x,y);
F = (X.^2+Y-11).^2 + (X + Y.^2 - 7).^2;

% you'll want to adjust this to better fit the ROI
%v = [0:2:10 10:10:100 100:20:200] 

% plot just the ROI
feasible = (X>=0) & (Y>=0) & (X+2*Y<=2);
F(~feasible) = NaN;
contour(X,Y,F,20,'linewidth',2); axis equal

Alternatively, this is often recommended, but I honestly have never used it and don't know how well it's suited for a 2D contour:

https://www.mathworks.com/matlabcentral/fileexchange/9261-plot-2d-3d-region

[Telema Harry]

Thank you for the detailed response.

Please I have one more trival question. I have several contour plots and I would like to understand it so I can easiliy plot them. Please what does this line of code mean: [1 1 -1 -1]*5,[-1 1 1 -1]*5, [5 -5],[-1.5 3.5]. I suspect, it is related to the axis.

[DGM]

the function line() plots a polyline between x and y points specified in two vectors. So

line([5 -5],[-1.5 3.5],'linestyle','--','color','k');

plots a diagonal line from (5,-1.5) to (-5,3.5). Similarly,

fill([1 1 -1 -1]*5,[-1 1 1 -1]*5,'w','facealpha',0.8);

plots a filled polygon whose vertices are coincident with the corners of the plot region. (a rectangle in this case)