How to show the Graphical Solution Method for an Optimization Problem

I am atempting to solve an Optimization problem using a graphical approach so that a solution can be observed. I do not need to solve the problem explicitly, but instead create a graph showing the objective function and the constaints placed on the system. I found a MathWorks video outlining how to approach and solve this type of problem. In the video a command is used called "visualizeProblem" which appears to create the graphical solution that I am trying to create. However, when I call this function it displays an error "Unrecognized function or variable 'visualizeProblem'." (A link to the video is attached below for reference.) I cannot find any doccumentation on this function or any potential replacements, and following the video, I believe I have the correct. As follows is my code:

prob = optimproblem;

x = optimvar("x_1","LowerBound",0,"UpperBound",10);
y = optimvar("x_2","LowerBound",0,"UpperBound",10);

prob.Objective = 4*x.^2 * y.^2;

cond1 = x + y <= 8;
cond2 = y <= 4;
cond3 = x >= 0;
cond4 = y >= 0;

prob.Constraints = cond1;
prob.Constraints = cond2;
prob.Constraints = cond3;
prob.Constraints = cond4;

showproblem(prob)

visualizeProblem

And I am atempting to achieve something that looks like this: (Note: This is not the same problem as shown above, this is the example graph from the MathWorks video I am referencing)

The video can be found here: https://www.mathworks.com/videos/part-4-problem-based-nonlinear-programming-1549458887351.html

Thank you in advance

[Sujoy Barua]

https://www.mathworks.com/help/optim/ug/optimization-toolbox-tutorial.html

Answer 1

[Matt J]

All I see in the figure is a contour plot of the objective. If that's all you need, you can use fcontour, e.g.,

fcontour(@(x,y) 4*x.^2 .* y.^2,[0,10],'LevelList',0:2:20)

Obviously, you can overaly contours of the constraint functions on this in a similar manner.

[Perry Marvin]

Not quite what I'm after, I need to have the objective function and the constraints on the plot.

[Matt J]

You can use hold on and hold off to overlay any additional plots you need. I'm pretty certain that's all that visualizeProblem was doing there..

[Perry Marvin]

I understand I can plot each individually, but I am asking if there is a way to plot the optimization problem. The code above sets up an optimization problem and the showproblem outputs the objective and the constraints. Is there a simple builtin command that plots that problem

[Matt J]

No, there is no built-in command. The visualizeProblem in the video was almost certainly a user-defined script that they forgot to provide. Notice that it didn't take any input arguments that let you specify an optimization problem.

Answer 2

[Sujoy Barua]

https://www.mathworks.com/help/optim/ug/optimization-toolbox-tutorial.html