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### How do I find the minimum-area ellipse that encloses a set of points?

Theory The 1997 paper "Smallest Enclosing Ellipses -- Fast and Exact" by Gärtner and Schönherr addresses this question. The same authors provide a C++ implementation in their 1998 paper &...
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### What is required of the objective function in order to use Gauss Newton method?

Just to clarify notation, I'll be discussing the Gauss-Newton method for the problem $\min \phi(x)=(1/2) \| F(x) \|_{2}^{2}$ with the search direction $p$ computed as the solution to the linear ...
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### How do I find the minimum-area ellipse that encloses a set of points?

With your formulation of the constraints, you can only produce ellipses where the semi-major and semi-minor axes are aligned with the coordinate axes, but it's clear from the figure that you attached ...
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