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.
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Tuy, H., Horst, R. 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 (1988). https://doi.org/10.1007/BF01580762
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DOI: https://doi.org/10.1007/BF01580762
Key words
- Global optimization
- nonconvex programming
- branch-and-bound
- restart procedure
- decomposition
- outer approximation
- concave minimization
- d.c. optimization