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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

Global Optimal Solution Outer Approximation Good Feasible Solution Recession Cone Supply Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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