# Restricted Simplicial Decomposition for Symmetric Convex Cost Flow Problems

Research output: Contribution to journalArticle

### 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) 363-381 19 American Journal of Mathematical and Management Sciences 12 4 https://doi.org/10.1080/01966324.1992.10737340 Published - Jan 1 1992

### Fingerprint

Nonlinear networks
Decomposition
Decompose
Arc of a curve
Costs
Simplicial Algorithm
Electrical Networks
Directed Network
Decomposition Algorithm
Strictly Convex
Spanning tree
Convex Hull
Computational Results
Objective function
Optimal Solution
Non-negative
Iteration
Water
Cycle
Standards

### All Science Journal Classification (ASJC) codes

• Applied Mathematics

### Cite this

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title = "Restricted Simplicial Decomposition for Symmetric Convex Cost Flow Problems",
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.",
author = "Ventura, {Jose Antonio}",
year = "1992",
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In: American Journal of Mathematical and Management Sciences, Vol. 12, No. 4, 01.01.1992, p. 363-381.

Research output: Contribution to journalArticle

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AU - Ventura, Jose Antonio

PY - 1992/1/1

Y1 - 1992/1/1

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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.

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