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KKT-based primal-dual exactness conditions for the Shor relaxation

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  • M. Locatelli

    (Università degli Studi di Parma)

Abstract

In this work we present some exactness conditions for the Shor relaxation of diagonal (or, more generally, diagonalizable) QCQPs, which extend the conditions introduced in different recent papers about the same topic. It is shown that the Shor relaxation is equivalent to two convex quadratic relaxations. Then, sufficient conditions for the exactness of the relaxations are derived from their KKT systems. It will be shown that, in some cases, by this derivation previous conditions in the literature, which can be viewed as dual conditions, since they only involve the Lagrange multipliers appearing in the KKT systems, can be extended to primal-dual conditions, which also involve the primal variables appearing in the KKT systems.

Suggested Citation

  • M. Locatelli, 2023. "KKT-based primal-dual exactness conditions for the Shor relaxation," Journal of Global Optimization, Springer, vol. 86(2), pages 285-301, June.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:2:d:10.1007_s10898-022-01258-5
    DOI: 10.1007/s10898-022-01258-5
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    References listed on IDEAS

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    1. Jos F. Sturm & Shuzhong Zhang, 2003. "On Cones of Nonnegative Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 246-267, May.
    2. Amir Beck & Dror Pan, 2017. "A branch and bound algorithm for nonconvex quadratic optimization with ball and linear constraints," Journal of Global Optimization, Springer, vol. 69(2), pages 309-342, October.
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