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Characterizing Existence of Minimizers and Optimality to Nonconvex Quadratic Integrals

Author

Listed:
  • Fabián Flores-Bazán

    (Universidad de Concepción)

  • Luis González-Valencia

    (Universidad de Concepción
    Universidad Austral de Chile)

Abstract

Quadratic functions play an important role in applied mathematics. In this paper, we consider the problem of minimizing the integral of a (not necessarily convex) quadratic function in a bounded subset of nonnegative integrable functions defined on a finite-dimensional space that is not compact with respect to any (locally convex) topology in the space of integrable functions. We establish a complete description about the existence or nonexistence of solution in terms of the (strict) copositivity of the matrix involved in the integrand. In addition, we characterize optimality via the Hamiltonian function.

Suggested Citation

  • Fabián Flores-Bazán & Luis González-Valencia, 2021. "Characterizing Existence of Minimizers and Optimality to Nonconvex Quadratic Integrals," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 497-522, February.
  • Handle: RePEc:spr:joptap:v:188:y:2021:i:2:d:10.1007_s10957-020-01794-8
    DOI: 10.1007/s10957-020-01794-8
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    References listed on IDEAS

    as
    1. G. Crasta, 1998. "Existence of Minimizers for Nonconvex Variational Problems with Slow Growth," Journal of Optimization Theory and Applications, Springer, vol. 99(2), pages 381-401, November.
    2. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
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