New approaches for optimizing over the semimetric polytope

Mathematical Programming

Volumn 104, Issue 2-3, 2005, Pages 375-388

  Frangioni, Antonio ^a   Lodi, Andrea ^b   Rinaldi, Giovanni ^c  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF BOLOGNA   (Italy)

^c CNR   (Italy)

Author keywords

Lagrangian methods; Max cut; Network design; Semimetric polytope

Indexed keywords

ALGORITHMS; COMBINATORIAL MATHEMATICS; DIFFERENTIAL EQUATIONS; LINEAR PROGRAMMING; OPTIMIZATION;

LAGRANGIAN METHODS; MAX-CUT; NETWORK DESIGN; SEMIMETRIC POLYTOPE;

MATHEMATICAL PROGRAMMING;

EID: 25444441268     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-005-0620-5     Document Type: Article

References (23)

1. Bahiense, L., Maculan, N., Sagastizábal, C.: The volume algorithm revisited: relation with bundle methods. Mathematical Programming 94, 41-70 (2002)
2. Barahona, F., Anbil, R.: The Volume Algorithm: Producing primal solutions with a subgradient method. Mathematical Programming. 87, 385-400 (2000)
3. Barahona, F., Grötschel, M., Jünger, M., Reinelt, G.: An application of combinatorial optimization to statistical physics and circuit layout design. Operations Research 36, p. 493 (1988)
4. Barahona, F., Mahjoub, A.: On the cut polytope. Mathematical Programming 36, 157-173 (1986)
5. Boros, A., Hammer, P.: Pseudo-boolean optimization. Discrete Applied Mathematics 123, 155-225 (2002)
6. Crainic, T., Frangioni, A., Gendron, B.: Bundle-based relaxation methods for multicommodity capacitated fixed charge network design problems. Discrete Applied Mathematics 112, 73-99 (2001)
7. Deza, M., Laurent, M.: Geometry of Cuts and Metrics. Vol. 15 of Algorithms and Combinatorics, Springer-Verlag, Berlin, 1997
8. du Merle, O., Goffin, J.-L., Vial, J.-P., On Improvements to the Analytic Center Cutting Plane Method. Computational Optimization and Applications 11, 37-52 (1998)
9. Frangioni, A.: Solving semidefinite quadratic problems within nonsmooth optimization algorithms. Computers & Operations Research 21, 1099-1118 (1996)
10. Frangioni, A., Generalized Bundle Methods. SIAM Journal on Optimization 13, 117-156 (2002)
11. Frangioni, A., About lagrangian methods in integer optimization. Annals of Operations Research to appear (2005)
12. Frangioni, A., Gallo, G.: A bundle type dual-ascent approach to linear multicommodity min cost flow problems. INFORMS Journal on Computing 11, 370-393 (1999)
13. Frangioni, A., Lodi, A., Rinaldi, G.: Optimizing over semimetric polytopes. In: Integer Programming and Combinatorial Optimization - IPCO 2004, D. Bienstock and G. Nemhauser, (eds.), Vol. 3064 of Lecture Notes in Computer Science, Springer-Verlag, 2004, pp. 431-443
14. Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer Verlag, 1988
15. Guignard, M., Efficient cuts in Lagrangean 'Relax-and-Cut' schemes. European Journal of Operational Research 105, 216-223 (1998)
16. Guignard, M.: Lagrangean relaxation. TOP, 11, 151-228 (2003)
17. Hiriart-Urruty, J.-B., Lemaréchal, C.: Convex Analysis and Minimization Algorithms. Vol. 306 of Grundlehren Math. Wiss. Springer-Verlag, New York, 1993
18. Kiwiel, K.C.: Convergence of Approximate and Incremental Subgradient Methods for Convex Optimization. SIAM Journal on Optimization 14, 807-840 (2004)
19. Knuth, D.E.: The Stanford GraphBase: a platform for combinatorial computing. ACM Press, 1993
20. Lemaréchal, C.: Lagrangian relaxation In: Computational Combinatorial Optimization, M. Jünger and D. Naddef, (eds.), Springer-Verlag, Heidelberg, 2001, pp. 115-160
21. Liers, F., Jünger, M., Reinelt, G., Rinaldi, G.: Computing exact ground-states of hard Ising spin glass problems by branch-and-cut. in New Optimization Algorithms in Physics, A. Hartmann and H. Rieger,(eds.), Wiley-VCH Verlag, Berlin, 2004, pp. 47-69
22. Lomonosov, M.: Combinatorial approaches to multiflow problems. Discrete Applied Mathematics 11, 1-93 (1985)
23. Rinaldi, G.: Rudy. http://www-user.tu-chemnitz.de/~helmberg/sdp_software. html.