|
DSpace - Tor Vergata >
Facoltà di Ingegneria >
Dipartimento di Ingegneria dell'impresa >
Research reports (Enterprise Engineering) >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/2108/1445
|
Full metadata record
| DC Field | Value | Language |
|---|
| contributor.author | Grippo, L. | - |
| contributor.author | Palagi, L. | - |
| contributor.author | Piacentini, M. | - |
| contributor.author | Piccialli, V. | - |
| contributor.author | Rinaldi, G. | - |
| date.accessioned | 2010-11-03T11:49:03Z | - |
| date.available | 2010-11-03T11:49:03Z | - |
| date.issued | 2010-11-03T11:49:03Z | - |
| identifier.uri | http://hdl.handle.net/2108/1445 | - |
| description.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 interesting features: (a) it provides heuristic solutions to Max-Cut along with a guaranteed optimality error; (b) it runs with a O(n + m) memory requirement (where m is the number of edges of the graph), thus overcoming a serious drawback of interior point based methods that demand O(n2) memory. Exploiting the latter feature, we could run it on very large graphs with sizes of up to a million nodes, obtaining
very small optimality error bounds in reasonable computation times. | en |
| format.extent | 321278 bytes | - |
| format.mimetype | application/pdf | - |
| language.iso | en | en |
| relation.ispartofseries | Research Report | en |
| relation.ispartofseries | RR-13.10 | en |
| subject | Semidefinite programming | en |
| subject | low rank factorization | en |
| subject | unconstrained | en |
| subject | Max-Cut | en |
| subject | nonlinear programming | en |
| title | SpeeDP: A new algorithm to compute the SDP relaxations of Max-Cut for very large graphs | en |
| type | Technical Report | en |
| Appears in Collections: | Research reports (Enterprise Engineering)
|
Files in This Item:
| File |
Description |
Size | Format |
|---|
| SpeeDP_TR.pdf | | 313Kb | Adobe PDF | View/Open |
|
Show simple item record
All items in DSpace are protected by copyright, with all rights reserved.
|
