Journal of Global Optimization

, Volume 1, Issue 1, pp 23–36 | Cite as

Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms

  • Hoang Tuy


We investigate subdivision strategies that can improve the convergence and efficiency of some branch and bound algorithms of global optimization. In particular, a general class of so called weakly exhaustive simplicial subdivision processes is introduced that subsumes all previously known radial exhaustive processes. This result provides the basis for constructing flexible subdivision strategies that can be adapted to take advantage of various problem conditions.

Key words

Branch and bound global optimization subdivision strategy exhaustive and weakly exhaustive subdivision processes 


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  1. 1.
    Falk, J. E. and Soland, R. M. (1969), An Algorithm for Separable Nonconvex Programming Problems, Management Science 15, 550–569.Google Scholar
  2. 2.
    Hamami, M. and Jacobsen, S. E. (1988), Exhaustive Nondegenerate Conical Processes for Concave Minimization on Convex Polytope, Mathematics of Operations Research 13, 479–481.Google Scholar
  3. 3.
    Horst, R. (1976), An Algorithm for Nonconvex Programming Problems, Mathematical Programming 10, 312–321.Google Scholar
  4. 4.
    Horst, R. and Thoai, N. V. (1989), Modification, Implementation and Comparison of Three Algorithms for Globally Solving Linearly Constrained Concave Minimization Problems, Computing 42, 271–289.Google Scholar
  5. 5.
    Horst, R. and Tuy, H. (1990), Global Optimization (Deterministic Approaches), Springer-Verlag.Google Scholar
  6. 6.
    Kalantari, B. and Rosen, J. B. (1987), An Algorithm for Global Mimization of Linearly Constrained Concave Quadratic Functions, Mathematics of Operations Research 12, 544–562.Google Scholar
  7. 7.
    Thoai, N. V. and Tuy, H. (1980), Convergent Algorithm for Minimizing a Concave Function, Mathematics of Operations Research 5, 556–566.Google Scholar
  8. 8.
    Tuy, H. (1991), Normal Conical Algorithm for Concave Minimization, Mathematical Programming. Forthcoming.Google Scholar
  9. 9.
    Tuy, H. and Horst, R. (1988), Convergence and Restart in Branch and Bound Algorithms for Global Optimization. Application to Concave Minimization and D.C. Optimization Problems, Mathematical Programming 41, 161–183.Google Scholar
  10. 10.
    Tuy, H. and Horst, R. (submitted), The Geometric Complementarity Problem and Transcending Stationarity in Global Optimization.Google Scholar
  11. 11.
    Tuy, H., Khachaturov, V., and Utkin, S. (1987), A Class of Exhaustive Cone Splitting Procedures in Conical Algorithms for Concave Minimization, Optimization 18, 791–807.Google Scholar
  12. 12.
    Utkin, S., Khachaturov, V., and Tuy, H. (1988), On Conical Algorithms for Solving Concave Programming Problems and Some of Their Extensions, USSR Computational Mathematics and Mathematical Physics 28, 992–999.Google Scholar

Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Hoang Tuy
    • 1
  1. 1.Institute of MathematicsHanoiVietnam

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