On univariate function identification problems

On univariate function identification problems Applications in the areas of data fitting, forecasting, and estimation naturally lead to a rich class of constrained infinite-dimensional optimization problems over extended real-valued semicontinuous functions. We discuss a framework for dealing with such applications, even in the presence of nearly arbitrary constraints on the functions. We formulate computationally tractable approximating problems relying on piecewise polynomial semicontinuous approximations of the actual functions. The approximations enable the study of evolving problems caused by incrementally arriving data and other information. In contrast to an earlier more general treatment, we focus on optimization over functions defined on a compact interval of the real line, which still addresses a large number of applications. The paper provides an introduction to the subject through simplified derivations and illustrative examples. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Programming Springer Journals

On univariate function identification problems

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society (outside the USA)
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Mathematics of Computing; Numerical Analysis; Combinatorics; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics
ISSN
0025-5610
eISSN
1436-4646
D.O.I.
10.1007/s10107-017-1130-y
Publisher site
See Article on Publisher Site

Abstract

Applications in the areas of data fitting, forecasting, and estimation naturally lead to a rich class of constrained infinite-dimensional optimization problems over extended real-valued semicontinuous functions. We discuss a framework for dealing with such applications, even in the presence of nearly arbitrary constraints on the functions. We formulate computationally tractable approximating problems relying on piecewise polynomial semicontinuous approximations of the actual functions. The approximations enable the study of evolving problems caused by incrementally arriving data and other information. In contrast to an earlier more general treatment, we focus on optimization over functions defined on a compact interval of the real line, which still addresses a large number of applications. The paper provides an introduction to the subject through simplified derivations and illustrative examples.

Journal

Mathematical ProgrammingSpringer Journals

Published: Mar 8, 2017

References

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