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Mathematical Programming

, Volume 41, Issue 1–3, pp 161–183 | Cite as

Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and D.C. Optimization problems

  • Hoang Tuy
  • Reiner Horst
Article

Abstract

A general branch-and-bound conceptual scheme for global optimization is presented that includes along with previous branch-and-bound approaches also grid-search techniques. The corresponding convergence theory, as well as the question of restart capability for branch-and-bound algorithms used in decomposition or outer approximation schemes are discussed. As an illustration of this conceptual scheme, a finite branch-and-bound algorithm for concave minimization is described and a convergent branch-and-bound algorithm, based on the previous one, is developed for the minimization of a difference of two convex functions.

Key words

Global optimization nonconvex programming branch-and-bound restart procedure decomposition outer approximation concave minimization d.c. optimization 

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Copyright information

© The Mathematical Programming Society, Inc. 1988

Authors and Affiliations

  • Hoang Tuy
    • 1
  • Reiner Horst
    • 2
  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.Universität TrierTrierFR Germany

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