Displaying similar documents to “Strongly quasiconvex quadratic functions.”

Remarks on strongly Wright-convex functions

Nelson Merentes, Kazimierz Nikodem, Sergio Rivas (2011)

Annales Polonici Mathematici

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Some properties of strongly Wright-convex functions are presented. In particular it is shown that a function f:D → ℝ, where D is an open convex subset of an inner product space X, is strongly Wright-convex with modulus c if and only if it can be represented in the form f(x) = g(x)+a(x)+c||x||², x ∈ D, where g:D → ℝ is a convex function and a:X → ℝ is an additive function. A characterization of inner product spaces by strongly Wright-convex functions is also given.

On semidefinite bounds for maximization of a non-convex quadratic objective over the unit ball

Mustafa Ç. Pinar, Marc Teboulle (2006)

RAIRO - Operations Research

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We consider the non-convex quadratic maximization problem subject to the unit ball constraint. The nature of the norm structure makes this problem extremely hard to analyze, and as a consequence, the same difficulties are encountered when trying to build suitable approximations for this problem by some tractable convex counterpart formulations. We explore some properties of this problem, derive SDP-like relaxations and raise open questions.