Mathematical Programming

, Volume 48, Issue 1, pp 1–17

On multilevel iterative methods for optimization problems

  • E. Gelman
  • J. Mandel

DOI: 10.1007/BF01582249

Cite this article as:
Gelman, E. & Mandel, J. Mathematical Programming (1990) 48: 1. doi:10.1007/BF01582249


This paper is concerned with multilevel iterative methods which combine a descent scheme with a hierarchy of auxiliary problems in lower dimensional subspaces. The construction of auxiliary problems as well as applications to elasto-plastic model and linear programming are described. The auxiliary problem for the dual of a perturbed linear program is interpreted as a dual of perturbed aggregated linear program. Coercivity of the objective function over the feasible set is sufficient for the boundedness of the iterates. Equivalents of this condition are presented in special cases.

Key words

Coercivity quadratic programming linear programming aggregation relaxation multigrid methods 

Copyright information

© The Mathematical Programming Society, Inc. 1990

Authors and Affiliations

  • E. Gelman
    • 1
  • J. Mandel
    • 1
  1. 1.Computational Mathematics GroupUniversity of Colorado at DenverDenverUSA

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