# On nonlinear replicated networks.

Qüestiió (1985)

- Volume: 9, Issue: 1, page 55-74
- ISSN: 0210-8054

## Access Full Article

top## Abstract

top## How to cite

topEscudero, Laureano F.. "On nonlinear replicated networks.." Qüestiió 9.1 (1985): 55-74. <http://eudml.org/doc/40064>.

@article{Escudero1985,

abstract = {In this paper we describe a new type of network flow problem that basically consists of the classical transshipment problem with the following extensions: (1) The replication of a network by producing subnetworks with identical structure, such that they are linked by so-called linking arcs; (2) The objective function terms related to the linking arcs are nondifferentiable nonlinear functions. We also describe an implementation of a linearly constrained nonlinear programming algorithm which is fast and can solve large-scale replicated network flow problems; the major ideas incorporated are: (i) The sparsity and the structure of the constraints system is used to reduce the time and computer storage requirements; (ii) The new concept of independent superbasic sets is introduced, so that it allows to obtain in parallel independent pieces of the solution at each iteration; (iii) The predecessor, depth, transverse and reverse structures are specialized for the case of replicated networks; (iv) A bending, backtracking linesearch that allows to activate more than one basic-superbasic arc at each iteration; (v) A procedure for pricing nonbasic arcs in the presence of non-differentiable terms in the objective function.},

author = {Escudero, Laureano F.},

journal = {Qüestiió},

keywords = {Redes no lineales; Arboles; Grafos; Algoritmos},

language = {eng},

number = {1},

pages = {55-74},

title = {On nonlinear replicated networks.},

url = {http://eudml.org/doc/40064},

volume = {9},

year = {1985},

}

TY - JOUR

AU - Escudero, Laureano F.

TI - On nonlinear replicated networks.

JO - Qüestiió

PY - 1985

VL - 9

IS - 1

SP - 55

EP - 74

AB - In this paper we describe a new type of network flow problem that basically consists of the classical transshipment problem with the following extensions: (1) The replication of a network by producing subnetworks with identical structure, such that they are linked by so-called linking arcs; (2) The objective function terms related to the linking arcs are nondifferentiable nonlinear functions. We also describe an implementation of a linearly constrained nonlinear programming algorithm which is fast and can solve large-scale replicated network flow problems; the major ideas incorporated are: (i) The sparsity and the structure of the constraints system is used to reduce the time and computer storage requirements; (ii) The new concept of independent superbasic sets is introduced, so that it allows to obtain in parallel independent pieces of the solution at each iteration; (iii) The predecessor, depth, transverse and reverse structures are specialized for the case of replicated networks; (iv) A bending, backtracking linesearch that allows to activate more than one basic-superbasic arc at each iteration; (v) A procedure for pricing nonbasic arcs in the presence of non-differentiable terms in the objective function.

LA - eng

KW - Redes no lineales; Arboles; Grafos; Algoritmos

UR - http://eudml.org/doc/40064

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.