Abstract
This paper presents a variation of the restricted simplicial decomposition (RSD) algorithm especially designed for solving nonlinear network problems with unrestricted arc flows and an objective function that is separable, strictly convex and symmetric with respect to the origin. These problems have the drawback that the standard linear subproblem of RSD is unbounded. However, their optimal solution is in the convex hull of a set of spanning tree solutions. The proposed algorithm uses a new linearized subproblem with nonnegative arc costs in a directed network, thereby avoiding negative cycles and guaranteeing the generation of a spanning treeat each iteration. Computational results are presented for some large-scale electrical networks and water distribution problems.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 363-381 |
| Number of pages | 19 |
| Journal | American Journal of Mathematical and Management Sciences |
| Volume | 12 |
| Issue number | 4 |
| DOIs | |
| State | Published - Jan 1 1992 |
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All Science Journal Classification (ASJC) codes
- Business, Management and Accounting(all)
- Applied Mathematics
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Restricted Simplicial Decomposition for Symmetric Convex Cost Flow Problems. / Ventura, Jose Antonio.
In: American Journal of Mathematical and Management Sciences, Vol. 12, No. 4, 01.01.1992, p. 363-381.Research output: Contribution to journal › Article
TY - JOUR
T1 - Restricted Simplicial Decomposition for Symmetric Convex Cost Flow Problems
AU - Ventura, Jose Antonio
PY - 1992/1/1
Y1 - 1992/1/1
N2 - This paper presents a variation of the restricted simplicial decomposition (RSD) algorithm especially designed for solving nonlinear network problems with unrestricted arc flows and an objective function that is separable, strictly convex and symmetric with respect to the origin. These problems have the drawback that the standard linear subproblem of RSD is unbounded. However, their optimal solution is in the convex hull of a set of spanning tree solutions. The proposed algorithm uses a new linearized subproblem with nonnegative arc costs in a directed network, thereby avoiding negative cycles and guaranteeing the generation of a spanning treeat each iteration. Computational results are presented for some large-scale electrical networks and water distribution problems.
AB - This paper presents a variation of the restricted simplicial decomposition (RSD) algorithm especially designed for solving nonlinear network problems with unrestricted arc flows and an objective function that is separable, strictly convex and symmetric with respect to the origin. These problems have the drawback that the standard linear subproblem of RSD is unbounded. However, their optimal solution is in the convex hull of a set of spanning tree solutions. The proposed algorithm uses a new linearized subproblem with nonnegative arc costs in a directed network, thereby avoiding negative cycles and guaranteeing the generation of a spanning treeat each iteration. Computational results are presented for some large-scale electrical networks and water distribution problems.
UR - http://www.scopus.com/inward/record.url?scp=84952207313&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84952207313&partnerID=8YFLogxK
U2 - 10.1080/01966324.1992.10737340
DO - 10.1080/01966324.1992.10737340
M3 - Article
VL - 12
SP - 363
EP - 381
JO - American Journal of Mathematical and Management Sciences
JF - American Journal of Mathematical and Management Sciences
SN - 0196-6324
IS - 4
ER -