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

Author

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

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.

Suggested Citation

  • Chieu, N.H. & Jeyakumar, V. & Li, G., 2020. "Convexifiability of continuous and discrete nonnegative quadratic programs for gap-free duality," European Journal of Operational Research, Elsevier, vol. 280(2), pages 441-452.
    • Handle: RePEc:eee:ejores:v:280:y:2020:i:2:p:441-452
    DOI: 10.1016/j.ejor.2019.08.009
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    Cited by:

    1. Thai Doan Chuong, 2020. "Semidefinite Program Duals for Separable Polynomial Programs Involving Box Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 289-299, April.

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