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Indefinite Abstract Splines with a Quadratic Constraint

Author

Listed:
  • Santiago Gonzalez Zerbo

    (Concejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
    Universidad de Buenos Aires)

  • Alejandra Maestripieri

    (Concejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
    Universidad de Buenos Aires)

  • Francisco Martínez Pería

    (Concejo Nacional de Investigaciones Científicas y Técnicas (CONICET)
    Universidad Nacional de La Plata)

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.

Suggested Citation

  • Santiago Gonzalez Zerbo & Alejandra Maestripieri & Francisco Martínez Pería, 2020. "Indefinite Abstract Splines with a Quadratic Constraint," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 209-225, July.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:1:d:10.1007_s10957-020-01692-z
    DOI: 10.1007/s10957-020-01692-z
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    References listed on IDEAS

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    1. R. Schöne & T. Hanning, 2012. "Least Squares Problems with Absolute Quadratic Constraints," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-12, September.
    2. Harish Palanthandalam-Madapusi & Tobin Van Pelt & Dennis Bernstein, 2009. "Matrix pencils and existence conditions for quadratic programming with a sign-indefinite quadratic equality constraint," Computational Optimization and Applications, Springer, vol. 45(4), pages 533-549, December.
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