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Exactness conditions for an SDP relaxation of the extended trust region problem

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Abstract

In this paper we show that a standard SDP relaxation for so called extended trust-region problem is equivalent to a convex quadratic problem, with a linear objective and constraint functions and some additional simple convex quadratic constraints. Through this equivalence, new conditions, generalizing the ones existing in the literature, under which the SDP relaxation is exact, are introduced.

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Acknowledgments

The author is grateful to two anonymous reviewers whose suggestions helped to improve an earlier version of the work.

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Authors and Affiliations

  1. Dipartimento di Ingegneria dell’Informazione, Università di Parma, Via G.P. Usberti, 181/A, 43124, Parma, Italy

    Marco Locatelli

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  1. Marco Locatelli
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Correspondence to Marco Locatelli.

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Locatelli, M. Exactness conditions for an SDP relaxation of the extended trust region problem. Optim Lett 10, 1141–1151 (2016). https://doi.org/10.1007/s11590-016-1001-0

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  • DOI: https://doi.org/10.1007/s11590-016-1001-0

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