# Separable convexification and DCA techniques for capacity and flow assignment problems

P. Mahey; Thai Q. Phong; H. P.L. Luna

RAIRO - Operations Research (2010)

- Volume: 35, Issue: 2, page 269-281
- ISSN: 0399-0559

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topMahey, P., Phong, Thai Q., and Luna, H. P.L.. "Separable convexification and DCA techniques for capacity and flow assignment problems." RAIRO - Operations Research 35.2 (2010): 269-281. <http://eudml.org/doc/197823>.

@article{Mahey2010,

abstract = {
We study a continuous version of the capacity and flow assignment problem
(CFA) where the design cost is combined with an average delay measure
to yield a non convex objective function coupled with multicommodity flow
constraints. A separable convexification of each arc cost function is proposed
to obtain approximate feasible solutions within easily computable gaps from
optimality. On the other hand, DC (difference of convex functions) programming can be used
to compute accurate upper bounds and reduce the gap.
The technique is shown to be effective when topology is assumed
fixed and capacity expansion on some arcs is considered.
},

author = {Mahey, P., Phong, Thai Q., Luna, H. P.L.},

journal = {RAIRO - Operations Research},

keywords = {Network design; DC optimization; capacity and flow assignment.},

language = {eng},

month = {3},

number = {2},

pages = {269-281},

publisher = {EDP Sciences},

title = {Separable convexification and DCA techniques for capacity and flow assignment problems},

url = {http://eudml.org/doc/197823},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Mahey, P.

AU - Phong, Thai Q.

AU - Luna, H. P.L.

TI - Separable convexification and DCA techniques for capacity and flow assignment problems

JO - RAIRO - Operations Research

DA - 2010/3//

PB - EDP Sciences

VL - 35

IS - 2

SP - 269

EP - 281

AB -
We study a continuous version of the capacity and flow assignment problem
(CFA) where the design cost is combined with an average delay measure
to yield a non convex objective function coupled with multicommodity flow
constraints. A separable convexification of each arc cost function is proposed
to obtain approximate feasible solutions within easily computable gaps from
optimality. On the other hand, DC (difference of convex functions) programming can be used
to compute accurate upper bounds and reduce the gap.
The technique is shown to be effective when topology is assumed
fixed and capacity expansion on some arcs is considered.

LA - eng

KW - Network design; DC optimization; capacity and flow assignment.

UR - http://eudml.org/doc/197823

ER -

## References

top- A. Balakrishnan and S.C. Graves, A composite algorithm for a concave-cost network flow problem. Networks19 (1989) 175-202. Zbl0673.90034
- D.P. Bertsekas and R.G. Gallager, Data Networks. Prentice-Hall (1987).
- J.E. Falk, Lagrange multipliers and nonconvex programs. SIAM J. Control Optim.7 (1969) 534-545. Zbl0184.44404
- L. Fratta, M. Gerla and L. Kleinrock, The flow deviation method: an approach to store-and-forward communication network design. Networks3 (1973) 97-133. Zbl1131.90321
- B. Gavish, Augmented Lagrangian based bounds for centralized network design. IEEE Trans. Comm.33 (1985) 1247-1257.
- B. Gavish and K. Altinkemer, Backbone network design tools with economic tradeoffs. ORSA J. Comput.2/3 (1990) 236-252. Zbl0755.90024
- B. Gavish and I. Neuman, A system for routing and capacity assignment in computer communication networks. IEEE Trans. Comm.37 (1989) 360-366.
- M. Gerla, The Design of Store-and-forward Networks for Computer Communications. Ph.D. Thesis, UCLA (1973).
- M. Gerla and L. Kleinrock, On the topological design of distributed computer networks. IEEE Trans. Comm.25 (1977) 48-60.
- M. Gerla, J.A.S. Monteiro and R. Pazos, Topology design and bandwith allocation in ATM nets. IEEE J. Selected Areas in Communications7 (1989) 1253-1261.
- J.B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms. Springer-Verlag (1993).
- H. Konno, P.T. Thach and H. Tuy, Optimization on Low Rank Nonconvex Structures. Kluwer Academic Publishers, Dordrecht (1997). Zbl0879.90171
- H.P.L. Luna and P. Mahey, Bounds for global optimization of capacity expansion and flow assignment problems. Oper. Res. Lett.26 (2000) 211-216. Zbl0960.90055
- P. Mahey, A. Benchakroun and F. Boyer, Capacity and flow assignment of data networks by generalized Benders decomposition. J. Global Optim. (to appear). Zbl1002.90082
- P. Mahey, A. Ouorou, L. LeBlanc and J. Chifflet, A new proximal decomposition algorithm for routing in telecommunications networks. Networks31 (1998) 227-238. Zbl1015.90020
- A. Ouorou, P. Mahey and J.P. Vial, A survey of algorithms for convex multicommodity flow problems. Management Sci.46 (2000) 126-147. Zbl1231.90110
- P.D. Tao and L.T.H. An, Convex analysis approach to dc programming: Theory, algorithms and applications. Acta Math. Vietnam.22 (1997) 289-355. Zbl0895.90152
- N.T. Quang, Une approche dc en optimisation dans les réseaux. Algorithmes, codes et simulations numériques. Doct. Thesis, Univ. Rouen (1999).
- B. Sanso, M. Gendreau and F. Soumis, An algorithm for network dimensioning under reliability considerations. Ann. Oper. Res.36 (1992) 263-274. Zbl0825.90377
- H. Tuy, S. Ghannadan, A. Migdalas and P. Varbrand, A strongly polynomial algorithm for a concave production-transportation problem with a fixed number of nonlinear variables. Math. Programming72 (1996) 229-258. Zbl0853.90116
- R. Wong, Introduction and recent advances in network design: Models and algorithms, in Transportation Planning Models, edited by M. Florian. Elsevier-North-Holland Publ. (1984). Zbl0594.90086

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