SpeeDP

 swMATH ID: 7003 Software Authors: Grippo, Luigi; Palagi, Laura; Piacentini, Mauro; Piccialli, Veronica; Rinaldi, Giovanni Description: SpeeDP: an algorithm to compute SDP bounds for very large max-cut instances 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 non-convex 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. We further include SpeeDP within a simply modified version of the Goemans-Williamson algorithm and we show that the corresponding heuristic SpeeDP-MC can generate high-quality cuts for very large, sparse graphs of size up to a million nodes in a few hours. Homepage: http://www.dis.uniroma1.it/~palagi/papers10/SpeeDP.pdf Keywords: low rank factorization; unconstrained binary quadratic programming; max-cut; nonlinear programming Related Software: Biq Mac; COL; Algorithm 769; Algorithm 815; Tabu search; DIMACS; TTTPLOTS; CirCut; SDPA; PERL; GRASP; QAPLIB; QuadProgBB; Ipopt; YALMIP; CPLEX; CSDP; PRMLT; LIBSVM; Benchmarks for Optimization Software Referenced in: 4 Publications
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Referenced by 12 Authors

 2 Palagi, Laura 1 De Santis, Marianna 1 Dellepiane, Umberto 1 Dong, Hongbo 1 Festa, Paola 1 Grippo, Luigi 1 Liuzzi, Giampaolo 1 Lucidi, Stefano 1 Piacentini, Mauro 1 Piccialli, Veronica 1 Rinaldi, Francesco 1 Rinaldi, Giovanni

Referenced in 4 Serials

 1 European Journal of Operational Research 1 Mathematical Programming. Series A. Series B 1 SIAM Journal on Optimization 1 Mathematical Programming Computation

Referenced in 2 Fields

 4 Operations research, mathematical programming (90-XX) 1 Statistics (62-XX)