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Please use this identifier to cite or link to this item: http://hdl.handle.net/2108/1445

Title: SpeeDP: A new algorithm to compute the SDP relaxations of Max-Cut for very large graphs
Authors: Grippo, L.
Palagi, L.
Piacentini, M.
Piccialli, V.
Rinaldi, G.
Keywords: Semidefinite programming
low rank factorization
unconstrained
Max-Cut
nonlinear programming
Issue Date: 3-Nov-2010
Series/Report no.: Research Report
RR-13.10
Abstract: We consider low-rank semidefinite programming (LRSDP) relaxations of unconstrained {−1, 1} quadratic problems (or, equivalently, of Max-Cut problems) that can be formulated as the nonconvex nonlinear programming problem of minimizing a quadratic function subject to separable quadratic equality constraints. We prove the equivalence of the LRSDP problem with the unconstrained minimization of a new merit function and we define an efficient and globally convergent algorithm, called SpeeDP, for finding critical points of the LRSDP problem. We provide evidence of the effectiveness of SpeeDP by comparing it with other existing codes on an extended set of instances of the Max-Cut problem. When the rank of solution matrix is bounded by a given value (in-dependent on the problem size n), SpeeDP is still able to provide a valid upper bound for Max-Cut. This feature makes it possible to design an algorithm, called SpeeDP-MC and based on the Goemans-Williamson heuristic, that has two interestin...
URI: http://hdl.handle.net/2108/1445
Appears in Collections:Research reports (Enterprise Engineering)

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