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

Authors:
Luigi Grippo;Laura Palagi;Veronica Piccialli
Affiliations:
Dipartimento di Informatica e Sistemistica "A. Ruberti", Sapienza Università di Roma, Rome, Italy 00185;Dipartimento di Informatica e Sistemistica "A. Ruberti", Sapienza Università di Roma, Rome, Italy 00185;Dipartimento di Informatica e Sistemistica "A. Ruberti", Sapienza Università di Roma, Rome, Italy 00185
Venue:
Journal of Global Optimization
Year:
2009

Citing 6
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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.