On nonlinear replicated networks.

Escudero, 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 -