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 semi- definite 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.
Grippo, L., Palagi, L., Piccialli, V. (2009). Necessary and sufficient global optimality conditions for NLP reformulations of linear SDP problems. JOURNAL OF GLOBAL OPTIMIZATION, 44, 339-348 [10.1007/s10898-008-9328-4].
Necessary and sufficient global optimality conditions for NLP reformulations of linear SDP problems
PICCIALLI, VERONICA
2009-01-01
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 semi- definite 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.File in questo prodotto:
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