Decomposition of Large Scale Problems

  • Reiner Horst
  • Hoang Tuy

Abstract

In many problems of large size encountered in applications, the constraints are linear, while the objective function is a sum of two parts: a linear part involving most of the variables of the problem, and a concave part involving only a relatively small number of variables. More precisely, these problems have the form
$$ {\text{minimize }}f(x) + dy\quad {\text{subject to }}(x,y) \in \Omega \subset {R^n} \times {R^h} $$
(P)
where f: ℝn → ℝ is a concave function, Ω is a polyhedron, d and y are vectors in ℝh, and n is generally much smaller than h.

Keywords

Transportation Lime Hull Tated Rosen 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Reiner Horst
    • 1
  • Hoang Tuy
    • 2
  1. 1.Department of MathematicsUniversity of TrierTrierGermany
  2. 2.Institute of MathematicsVien Toan HocHanoiVietnam

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