Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/307569 
Year of Publication: 
2023
Citation: 
[Journal:] Computational Optimization and Applications [ISSN:] 1573-2894 [Volume:] 85 [Issue:] 2 [Publisher:] Springer US [Place:] New York, NY [Year:] 2023 [Pages:] 409-439
Publisher: 
Springer US, New York, NY
Abstract: 
We revisit the problem of computing optimal spline approximations for univariate least-squares splines from a combinatorial optimization perspective. In contrast to most approaches from the literature we aim at globally optimal coefficients as well as a globally optimal placement of a fixed number of knots for a discrete variant of this problem. To achieve this, two different possibilities are developed. The first approach that we present is the formulation of the problem as a mixed-integer quadratically constrained problem, which can be solved using commercial optimization solvers. The second method that we propose is a branch-and-bound algorithm tailored specifically to the combinatorial formulation. We compare our algorithmic approaches empirically on both, real and synthetic curve fitting data sets from the literature. The numerical experiments show that our approach to tackle the least-squares spline approximation problem with free knots is able to compute solutions to problems of realistic sizes within reasonable computing times.
Subjects: 
Spline approximation
Least-squares spline approximation
Branch-and-bound
Global optimization
Curve fitting
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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