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Separable convexification and DCA techniques for capacity and flow assignment problems

Published online by Cambridge University Press:  15 August 2002

P. Mahey ,
Thai Q. Phong  and
H. P.L. Luna
P. Mahey
Affiliation:
LIMOS-CNRS, Université Blaise Pascal, Aubière, France; mahey@sp.isima.fr. This work was partially supported by France Telecom RD, CTI99-1B-281.
Thai Q. Phong
Affiliation:
LIMOS-CNRS, Université Blaise Pascal, Aubière, France; tqphong@sp.isima.fr. : Da Nang University, Vietnam.
H. P.L. Luna
Affiliation:
DCC-ICeX, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brasil; pacca@dcc.ufmg.br.
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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.

Keywords

Network designDC optimizationcapacity and flow assignment.
Type
Research Article
Information
RAIRO - Operations Research , Volume 35 , Issue 2: ROADEF'99 , April 2001 , pp. 269 - 281
Copyright
© EDP Sciences, 2001

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