Indefinite Abstract Splines with a Quadratic Constraint

Santiago Gonzalez Zerbo (), Alejandra Maestripieri () and Francisco Martínez Pería ()
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Santiago Gonzalez Zerbo: Concejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
Alejandra Maestripieri: Concejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
Francisco Martínez Pería: Concejo Nacional de Investigaciones Científicas y Técnicas (CONICET)

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 1, No 11, 209-225

Abstract: Abstract 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.

Keywords: Abstract splines; Krein spaces; Quadratically constrained quadratic programming; Linear quadratic regulator; 46C20; 47B50; 65D07; 65D10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01692-z

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