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Mathematical Programming

, Volume 62, Issue 1–3, pp 239–260 | Cite as

A generalized Dantzig—Wolfe decomposition principle for a class of nonconvex programming problems

  • Phan Thien Thach
  • Hiroshi Konno
Article

Abstract

Since Dantzig—Wolfe's pioneering contribution, the decomposition approach using a pricing mechanism has been developed for a wide class of mathematical programs. For convex programs a linear space of Lagrangean multipliers is enough to define price functions. For general mathematical programs the price functions could be defined by using a subclass of nondecreasing functions. However the space of nondecreasing functions is no longer finite dimensional. In this paper we consider a specific nonconvex optimization problem min {f(x):h j (x)⩽g(x),j=1, ⋯,m, xX}, wheref(·),h j (·) andg(·) are finite convex functions andX is a closed convex set. We generalize optimal price functions for this problem in such a way that the parameters of generalized price functions are defined in a finite dimensional space. Combining convex duality and a nonconvex duality we can develop a decomposition method to find a globally optimal solution.

Key words

Decomposition price functions global optimization 

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Copyright information

© The Mathematical Programming Society, Inc. 1993

Authors and Affiliations

  • Phan Thien Thach
    • 1
  • Hiroshi Konno
    • 1
  1. 1.Institute of Human and Social SciencesTokyo Institute of TechnologyTokyoJapan

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