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

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 relaxat...

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Bibliographic Details
Published inJournal of global optimization Vol. 86; no. 2; pp. 285 - 301
Main Author Locatelli, M.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2023
Springer
Springer Nature B.V
Subjects
Computer Science
Lagrange multiplier
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Quadratic programming
Real Functions
Variables
Convex relaxations
Quadratically Constrained Quadratic Programming
Exactness conditions
Shor relaxation
Online AccessGet full text
ISSN0925-5001
1573-2916
DOI10.1007/s10898-022-01258-5

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Summary: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.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01258-5