Abstract
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.
Similar content being viewed by others
References
Falk, J. E. and Soland, R. M. (1969), An Algorithm for Separable Nonconvex Programming Problems, Management Science 15, 550–569.
Hamami, M. and Jacobsen, S. E. (1988), Exhaustive Nondegenerate Conical Processes for Concave Minimization on Convex Polytope, Mathematics of Operations Research 13, 479–481.
Horst, R. (1976), An Algorithm for Nonconvex Programming Problems, Mathematical Programming 10, 312–321.
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.
Horst, R. and Tuy, H. (1990), Global Optimization (Deterministic Approaches), Springer-Verlag.
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.
Thoai, N. V. and Tuy, H. (1980), Convergent Algorithm for Minimizing a Concave Function, Mathematics of Operations Research 5, 556–566.
Tuy, H. (1991), Normal Conical Algorithm for Concave Minimization, Mathematical Programming. Forthcoming.
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.
Tuy, H. and Horst, R. (submitted), The Geometric Complementarity Problem and Transcending Stationarity in Global Optimization.
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.
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.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tuy, H. Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms. J Glob Optim 1, 23–36 (1991). https://doi.org/10.1007/BF00120663
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00120663