- Parametrize an ellipse with a vector x, whose components represent the eccentricity, size, and center (4 dimensions), or any other parametrization you like.
- Figure out how you can tell whether, for a given x vector, the ellipse is inside the region. In other words, create a function c(x) that is negative when the entire ellipse is in the region, and is positive when some of the ellipse sticks out of the region, and is smooth.
- Write the objective function as negative the area of the ellipse, and the nonlinear inequality constraint is c(x).
- Call fmincon from a variety of initial values.
Good luck,
Alan Weiss
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