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

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

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Article ID: iaor200971238
Country: Netherlands
Volume: 44
Issue: 3
Start Page Number: 339
End Page Number: 348
Publication Date: Jul 2009
Journal: Journal of Global Optimization
Authors: , ,
Keywords: programming (semidefinite)
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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