Indefinite Abstract Splines with a Quadratic Constraint

We study an extension to Krein spaces of the abstract interpolating spline problem in Hilbert spaces, introduced by M. Atteia. This is a quadratically constrained quadratic programming problem, where the objective function is not convex, while the equality constraint is sign indefinite. We character...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 186; no. 1; pp. 209 - 225
Main Authors: Gonzalez Zerbo, Santiago, Maestripieri, Alejandra, Martínez Pería, Francisco
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2020
Springer Nature B.V
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Constraints
Control theory
Engineering
Equality
Hilbert space
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Quadratic programming
Spline functions
Theory of Computation
Krein spaces
65D10
46C20
Quadratically constrained quadratic programming
47B50
Abstract splines
Linear quadratic regulator
65D07
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:We study an extension to Krein spaces of the abstract interpolating spline problem in Hilbert spaces, introduced by M. Atteia. This is a quadratically constrained quadratic programming problem, where the objective function is not convex, while the equality constraint is sign indefinite. We characterize the existence of solutions and, if there are any, we describe the set of solutions as the union of a family of affine manifolds parallel to a fixed subspace, which depend on the original data.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-020-01692-z