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

M. Locatelli ()
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M. Locatelli: Università degli Studi di Parma

Journal of Global Optimization, 2023, vol. 86, issue 2, No 1, 285-301

Abstract: 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.

Keywords: Quadratically Constrained Quadratic Programming; Shor relaxation; Convex relaxations; Exactness conditions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01258-5

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