Publications of Giovanni Rinaldi

This page shows all publications that appeared in the IASI annual research reports. Authors currently affiliated with the Institute are always listed with the full name.

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IASI Research Report n. 11-12  (Previous    Next)  

Grippo L., Palagi L., Piacentini M., Piccialli V., Giovanni Rinaldi

SpeeDP: An algorithm to compute SDP bounds for very large Max-Cut instances

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 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 an enhanced version of the Goemans-Williamson algorithm and we show that the corresponding heuristic SpeeDPMC can generate high-quality cuts for very large, sparse graphs of size up to a million nodes in a few hours.
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