Minimization of quadratic functions on convex sets without asymptotes

Juan Enrique Martínez-Legaz, Dominikus Noll, Wilfredo Sosa

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8 Citations (Scopus)


The classical Frank and Wolfe theorem states that a quadratic function which is bounded below on a convex polyhedron P attains its infimum on P. We investigate whether more general classes of convex sets F can be identified which have this Frank-and-Wolfe property. We show that the intrinsic characterizations of Frank-and-Wolfe sets hinge on asymptotic properties of these sets.
Original languageEnglish
Pages (from-to)623-641
JournalJournal of Convex Analysis
Issue number2
Publication statusPublished - 1 Jan 2018


  • Asymptotes
  • Complementarity problem
  • Conic asymptotes
  • Frank
  • Motzkin decomposition
  • Quadratic optimization problem
  • Wolfe theorem


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