Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations

García Ródenas, Ricardo and Marín Gracia, Angel and Patriksson, Michael (2011). Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations. "Computer and Operation Research", v. 38 (n. 3); pp. 591-604. ISSN 0305-0548. https://doi.org/10.1016/j.cor.2010.07.021.

Description

Title: Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations
Author/s:
  • García Ródenas, Ricardo
  • Marín Gracia, Angel
  • Patriksson, Michael
Item Type: Article
Título de Revista/Publicación: Computer and Operation Research
Date: March 2011
ISSN: 0305-0548
Volume: 38
Subjects:
Freetext Keywords: Simplicial decomposition, Nonlinear column generation, Convex minimization, Network flow problems
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Matemática Aplicada y Estadística [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

García et al. 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

More information

Item ID: 15270
DC Identifier: http://oa.upm.es/15270/
OAI Identifier: oai:oa.upm.es:15270
DOI: 10.1016/j.cor.2010.07.021
Deposited by: Memoria Investigacion
Deposited on: 05 Jun 2014 18:33
Last Modified: 21 Apr 2016 15:19
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