Characterizing Existence of Minimizers and Optimality to Nonconvex Quadratic Integrals

Fabián Flores-Bazán () and Luis González-Valencia ()
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Fabián Flores-Bazán: Universidad de Concepción
Luis González-Valencia: Universidad de Concepción

Journal of Optimization Theory and Applications, 2021, vol. 188, issue 2, No 10, 497-522

Abstract: 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.

Keywords: Nonconvex optimization; Quadratic optimization; Lyapunov theorem; Hamiltonian; Strong duality; 90C25; 90C20; 90C34; 90C46; 49J45 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-020-01794-8

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