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.
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Acknowledgements
The authors are indebted to two anonymous referees and to Associate Editor for their helpful remarks and suggestions that allowed us to improve the presentation of the paper. The research, for the first author, was supported in part by ANID-Chile through FONDECYT 118-1316 and PIA/Concurso Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento AFB170001.
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Communicated by Boris S. Mordukhovich.
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Flores-Bazán, F., González-Valencia, L. Characterizing Existence of Minimizers and Optimality to Nonconvex Quadratic Integrals. J Optim Theory Appl 188, 497–522 (2021). https://doi.org/10.1007/s10957-020-01794-8
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DOI: https://doi.org/10.1007/s10957-020-01794-8