Croatian Operational Research Review (CRORR), Vol. 1, 2010
ON THE SET-SEMIDEFINITE REPRESENTATION OF NONCONVEX QUADRATIC
PROGRAMS WITH CONE CONSTRAINTS
Gabriele Eichfelder
University of Erlangen-Nürnberg, Department of Mathematics
Martensstr. 3, D-91058 Erlangen, Germany, E-mail: [email protected]
Janez Povh1
Faculty of Information Studies in Novo Mesto
Novi trg 5, 8000 Novo mesto, Slovenia, E-mail: [email protected]
Abstract: The well-known result stating that any non-convex quadratic problem over the non-negative
orthant with some additional linear and binary constraints can be rewritten as linear problem over the cone of
completely positive matrices (Burer, 2009) is generalizes by replacing the non-negative orthant with
arbitrary closed convex and pointed cone. This set-semidefinite representation result implies new
semidefinite lower bounds for quadratic problems over the Bishop-Phelps cones, based on the Euclidian
norm.
set positivity, Bishop-Phelps cones
Key words:
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Supported by the Slovenian Research Agency (project no. 1000-08-210518).
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