Multivariate Epi-Splines and Evolving Function Identification Problems
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Authors
Royset, Johannes O.
Wets, Roger J-B
Subjects
function approximation
epi-splines
epi-convergence
infinite-dimensional optimization
shape restriction
constrained optimization
epi-splines
epi-convergence
infinite-dimensional optimization
shape restriction
constrained optimization
Advisors
Date of Issue
2016-04-15
Date
April 15, 2015
Publisher
Language
Abstract
The broad class of extended real-valued lower semicontinuous (lsc) functions on IRn captures
nearly all functions of practical importance in equation solving, variational problems, fitting, and
estimation. The paper develops piecewise polynomial functions, called epi-splines, that approximate
any lsc function to an arbitrary level of accuracy. Epi-splines provide the foundation for the solution
of a rich class of function identification problems that incorporate general constraints on the function
to be identified including those derived from information about smoothness, shape, proximity to other
functions, and so on. As such extrinsic information as well as observed function and subgradient values
often evolve in applications, we establish conditions under which the computed epi-splines converge
to the function we seek to identify. Numerical examples in response surface building and probability
density estimation illustrate the framework.
Type
Article
Description
Includes erratum
Series/Report No
Department
Operations Research (OR)
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
U. S. Army Research Laboratory and the U. S. Army Research Office grant 00101-80683
U. S. Army Research Laboratory and the U. S. Army Research Office grant W911NF-10-1-0246
U. S. Army Research Laboratory and the U. S. Army Research Office grant W911NF-12-1-0273
U. S. Army Research Laboratory and the U. S. Army Research Office grant W911NF-10-1-0246
U. S. Army Research Laboratory and the U. S. Army Research Office grant W911NF-12-1-0273
Funder
U. S. Army Research Laboratory and the U. S. Army Research Office grant 00101-80683
U. S. Army Research Laboratory and the U. S. Army Research Office grant W911NF-10-1-0246
U. S. Army Research Laboratory and the U. S. Army Research Office grant W911NF-12-1-0273
U. S. Army Research Laboratory and the U. S. Army Research Office grant W911NF-10-1-0246
U. S. Army Research Laboratory and the U. S. Army Research Office grant W911NF-12-1-0273
Format
Article-34 p./Erratum-3 p.
Citation
J.O. Royset and R. J-B Wets, 2016, "Multivariate Epi-Splines and Evolving Function Identification Problems," Set-Valued and Variational Analysis, to appear. Erratum.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.