Convexifiability of continuous and discrete nonnegative quadratic programs for gap-free duality

N.H. Chieu, V. Jeyakumar and G. Li

European Journal of Operational Research, 2020, vol. 280, issue 2, 441-452

Abstract: In this paper we show that a convexifiability property of nonconvex quadratic programs with nonnegative variables and quadratic constraints guarantees zero duality gap between the quadratic programs and their semi-Lagrangian duals. More importantly, we establish that this convexifiability is hidden in classes of nonnegative homogeneous quadratic programs and discrete quadratic programs, such as mixed integer quadratic programs, revealing zero duality gaps. As an application, we prove that robust counterparts of uncertain mixed integer quadratic programs with objective data uncertainty enjoy zero duality gaps under suitable conditions. Various sufficient conditions for convexifiability are also given.

Keywords: Global optimization; Quadratic optimization; Zero duality gaps; Mixed integer quadratic programs; Duality, (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:280:y:2020:i:2:p:441-452

DOI: 10.1016/j.ejor.2019.08.009

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