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Everyone good time of day!

Please use the function "fmincon" to minimize the ellipse area function of the form , containing 6 variables from the canonical equation of the second order curve.

Everything would be nice if A, B, C, D, E and F were independent and linearly limited, but this is not so. These coefficients are limited by several inequalities of the form . Each such inequality suggests that the point with the coordinates is inside a certain second-order curve (in this case, an ellipse). The number of such inequalities corresponds to the length of the array of points, and usually at least twelve of them.

In addition to these inequalities, there are also two invariants that exclude the possibility of obtaining any other second-order curve except the ellipse: и .

In "MatLab help," I saw examples of using the function "fmincon" together with linear constraints in the form of inequalities, but I would like to put NONLINEAR constraints.

I will be incredibly grateful for the help!

P.S. I apologize for my English, because I am from Russia and do not know it perfectly.

Alan Weiss
on 20 Oct 2020

I think that you are on the right track using fmincon. See the function reference page for details. Also, there is a topic on how to write nonlinear constraints.

Alan Weiss

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