Optimization problem with quadratic function

Hello everyone,

I hope someone could help me. This is the problem:

I have 12 points which are experimental measures, represented by 3 independent variables (x,y,z) and the fourth one that represents the density and it depends from the others: w= f(x,y,z). I need to:

-plot the data,

-obtain the quadratic fit function w, i.e. the function that describes the density,

-represent the isosurfaces where w is constant.

- Finally I need to minimize this quadratic function with no constraints.

Starting from

x = rand(12, 1);

y = rand(12, 1);

z = rand(12, 1);

w = rand(12, 1);

I found the quadratic function but I'm not sure how to represent the values of f(x,y,z) like isosurfaces and how to minimize it.

Thanks a lot!

Laura

Answer 1

[Matt J]

You can use isosurface() to plot and quadprog() to minimize.

[laura bagnale]

Thank you very much for your prompt reply!

I wrote the optimization problem like this:

p.Objective =p = optimproblem

p.Description = "minimization"

x = optimvar("x", "LowerBound", -1, "UpperBound",1);

y = optimvar("y", "LowerBound", -1, "UpperBound",1);

z = optimvar("z","LowerBound", -1, "UpperBound",1 );

p.Objective = -3.4614 +4.2699*z + -1.9757*y + 5.8535*x -2.0954*z.^2 -3.7708*y.^2 + -1.2299*x.^2 - 3.1261*y.*z - 0.9395*x.*z - 3.1720*x.*y

initialPt.x = 1;

initialPt.y = 1;

initialPt.z = 1;

hold on

[sol,fval,exitflag,outout] = solve(p,initialPt)

hold off + 2.8392*z + 0.5153*y + 0.7036*x -2.2113*z.^2 -0.1385*y.^2 + 0.3061*x.^2 - 0.5117*y.*z - 1.3679*x.*z - 0.0074*x.*y

It uses the quadprog solver.

Do you think that it could be correct?

I'm not sure how to use isosurface() to plot it.

Thank you

[Matt J]

It looks like you might have a few copy/paste errors in your post, but otherwise, yes, it looks correct. Also, since it is a non-convex quadratic, it might be a good idea to try multiple initialPts.

[laura bagnale]

Thanks a lot for your help and support!!

That was helpful!

Kind Regards,

Laura

[Matt J]

I'm glad, but please Accept-click the answer if the your question is now resolved.