Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets. (arXiv:2210.01919v1 [eess.SY] CROSS LISTED)

We consider estimating a compact set from finite data by approximating the
support function of that set via sublinear regression. Support functions
uniquely characterize a compact set up to closure of convexification, and are
sublinear (convex as well as positive homogeneous of degree one). Conversely,
any sublinear function is the support function of a compact set. We leverage
this property to transcribe the task of learning a compact set to that of
learning its support function. We propose two algorithms …

application arxiv data data-driven regression