Mathematical Programming Algorithms for Regression-based Nonlinear Filtering in Ir N

Constrained regression problems appear in the context of optimal nonlinear ltering, as well as in a variety of other contexts, e.g., chromatographic analysis in chemometrics and manufacturing , and spectral estimation. This paper presents novel mathematical programming algorithms for some important constrained regression problems in IR N. For brevity, we focus on four key problems, namely, locally monotonic regression (the optimal counterpart of iterated median lter-ing), and the related problem of piecewise monotonic regression, runlength-constrained regression (a useful segmentation and edge detection technique), and uni-and oligo-modal regression (of interest in chromatography and spectral estimation). The proposed algorithms are exact and ef-cient, and they also naturally suggest slightly suboptimal but very fast approximate algorithms, which may be preferable in practice.