Abstract
This note presents a new convergence property for each of two branch-and-bound algorithms for nonconvex programming problems (Falk-Soland algorithms and Horst algorithms). For each algorithm, it has been shown previously that, under certain conditions, whenever the algorithm generates an infinite sequence of points, at least one accumulation point of this sequence is a global minimum. We show here that, for each algorithm, in fact, under these conditions, every accumulation point of such a sequence is a global minimum.
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References
Falk, J. E., andSoland, R. M.,An Algorithm for Separable Nonconvex Programming Problems, Management Science, Vol. 15, pp. 550–569, 1969.
Horst, R.,An Algorithm for Nonconvex Programming Problems, Mathematical Programming, Vol. 10, pp. 312–321, 1976.
Horst, R., Private Communication, 1980.
Benson, H. P.,On the Convergence of Two Branch-and-Bound Algorithms for Nonconvex Programming Problems, University of Florida, Center for Econometrics and Decision Sciences, Discussion Paper No. 3, 1979.
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Communicated by G. Leitmann
The author would like to thank Professor R. M. Soland for his helpful comments concerning this paper.
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Benson, H.P. On the convergence of two branch-and-bound algorithms for nonconvex programming problems. J Optim Theory Appl 36, 129–134 (1982). https://doi.org/10.1007/BF00934342
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DOI: https://doi.org/10.1007/BF00934342