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**Harvard**

Garcia-Rodenas, R., Marin, A. och Patriksson, M. (2011) *Column generation algorithms for nonlinear optimization, II: Numerical investigations*.

** BibTeX **

@article{

Garcia-Rodenas2011,

author={Garcia-Rodenas, R. and Marin, A. and Patriksson, Michael},

title={Column generation algorithms for nonlinear optimization, II: Numerical investigations},

journal={Computers & Operations Research},

issn={0305-0548},

volume={38},

issue={3},

pages={591-604},

abstract={Garcia et al. [1] present a class of column generation (CG) algorithms for nonlinear programs. Its main motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be achieved, in much the same way as for the classic simplicial decomposition method; the main practical motivation is that within the class there are certain nonlinear column generation problems that can accelerate the convergence of a solution approach which generates a sequence of feasible points. This algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of these methods given in [1] with an experimental study focused on their computational efficiency. Three types of numerical experiments are conducted. The first group of test problems has been designed to study the parameters involved in these methods. The second group has been designed to investigate the role and the computation of the prolongation of the generated columns to the relative boundary. The last one has been designed to carry out a more complete investigation of the difference in computational efficiency between linear and nonlinear column generation approaches. In order to carry out this investigation, we consider two types of test problems: the first one is the nonlinear, capacitated single-commodity network flow problem of which several large-scale instances with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second one is a combined traffic assignment model.},

year={2011},

keywords={Simplicial decomposition, Nonlinear column generation, Convex, minimization, Network flow problems, restricted simplicial decomposition, traffic assignment problem, network equilibrium, combined modes, transportation },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 130675

A1 Garcia-Rodenas, R.

A1 Marin, A.

A1 Patriksson, Michael

T1 Column generation algorithms for nonlinear optimization, II: Numerical investigations

YR 2011

JF Computers & Operations Research

SN 0305-0548

VO 38

IS 3

SP 591

OP 604

AB Garcia et al. [1] present a class of column generation (CG) algorithms for nonlinear programs. Its main motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be achieved, in much the same way as for the classic simplicial decomposition method; the main practical motivation is that within the class there are certain nonlinear column generation problems that can accelerate the convergence of a solution approach which generates a sequence of feasible points. This algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of these methods given in [1] with an experimental study focused on their computational efficiency. Three types of numerical experiments are conducted. The first group of test problems has been designed to study the parameters involved in these methods. The second group has been designed to investigate the role and the computation of the prolongation of the generated columns to the relative boundary. The last one has been designed to carry out a more complete investigation of the difference in computational efficiency between linear and nonlinear column generation approaches. In order to carry out this investigation, we consider two types of test problems: the first one is the nonlinear, capacitated single-commodity network flow problem of which several large-scale instances with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second one is a combined traffic assignment model.

LA eng

DO 10.1016/j.cor.2010.07.021

LK http://dx.doi.org/10.1016/j.cor.2010.07.021

OL 30