Journal
OPTIMIZATION AND ENGINEERING
Volume 10, Issue 1, Pages 1-17Publisher
SPRINGER
DOI: 10.1007/s11081-008-9045-3
Keywords
Convex optimization; Piecewise-linear approximation; Data fitting
Categories
Funding
- MARCO Focus Center for Circuit and System Solutions [2003-CT-888]
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We consider the problem of fitting a convex piecewise-linear function, with some specified form, to given multi-dimensional data. Except for a few special cases, this problem is hard to solve exactly, so we focus on heuristic methods that find locally optimal fits. The method we describe, which is a variation on the K-means algorithm for clustering, seems to work well in practice, at least on data that can be fit well by a convex function. We focus on the simplest function form, a maximum of a fixed number of affine functions, and then show how the methods extend to a more general form.
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