On univariate function identification problems

• 成果类型: Article
• 署名作者: Royset, Johannes O.; Wets, Roger J. -B.
• 署名单位: United States Department of Defense; United States Navy; Naval Postgraduate School; University of California System; University of California Davis
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1130-y
• 发表日期: 2018
• 页码: 449-474
• 关键词: spline functions; approximation; interpolation

摘要

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.