Geometry – Largest Ellipse Inscribed in a Convex Polygon

Question

Considering a N edges convex 2D polygon called P.
Let's name its vertices $\{p_1, p_2, …, p_N\}$ described in a counter-clockwise order, with $p_i = (x_i, y_i)$

What would be, and how would one compute(preferably without optimization algorithm) the ellipse of biggest area E included in this polygon?

Answer 1

Start by converting the given polygon from a set of vertices to a set of linear inequalities. Then one can use convex optimization. From chapter 8 of Boyd & Vandenberghe's Convex Optimization:

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