Tractable Fitting with Convex Polynomials via Sum-of-Squares
A. Magnani, S. Lall, and S. Boyd
Proceedings of IEEE Conference on Decision and Control and European
Control Conference (CDC-ECC), p1672-1677, December 2005.
We consider the problem of fitting given data ,
where
and f$.
A technique to solve
this problem using sum of squares polynomials is presented. This technique is
extended to enforce convexity of f only on a specified region. Also, an
algorithm to fit the convex hull of a set of points with a convex sublevel set
of a polynomial is presented. This problem is a natural extension of the
problem of finding the minimum volume ellipsoid covering a set. The algorithm,
like that for the minimum volume ellipsoid problem, has the property of being
invariant to affine coordinate transformations. We generalize this technique to
fit arbitrary unions and intersections of polynomial sublevel sets.
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