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Necessary and sufficient global optimality conditions for NLP reformulations of linear SDP problems

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Abstract

In this paper we consider the standard linear SDP problem, and its low rank nonlinear programming reformulation, based on a Gramian representation of a positive semidefinite matrix. For this nonconvex quadratic problem with quadratic equality constraints, we give necessary and sufficient conditions of global optimality expressed in terms of the Lagrangian function.

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Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica “A. Ruberti”, Sapienza Università di Roma, via Ariosto 25, 00185, Rome, Italy

    Luigi Grippo, Laura Palagi & Veronica Piccialli

Authors
  1. Luigi Grippo
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  2. Laura Palagi
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  3. Veronica Piccialli
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Correspondence to Veronica Piccialli.

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Grippo, L., Palagi, L. & Piccialli, V. Necessary and sufficient global optimality conditions for NLP reformulations of linear SDP problems. J Glob Optim 44, 339–348 (2009). https://doi.org/10.1007/s10898-008-9328-4

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  • DOI: https://doi.org/10.1007/s10898-008-9328-4

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