Abstract
We propose a general cutting method for conditional minimization of continuous functions. We calculate iteration points by partially embeddimg the admissible set in approximating polyhedral sets. We describe the features of the proposed method and prove its convergence. The constructed general method does not imply the inclusion of each of approximating sets in the previous one. This feature allows us to construct cutting algorithms which periodically drop any additional restrictions which occur in the solution process.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. P. Bulatov, Embedding Methods in Optimization Problems (Nauka, Novosibirsk, 1977) [in Russian].
I. Ya. Zabotin, “Some Embedding-Cutting Algorithms for Mathematical Programming Problems,” Izv. Irkutsk. Gos. Univ., Ser. Matem. 4(2), 91–101 (2011).
U. I. Zangwill, Nonlinear Programming: A Unified Approach (Prentice-Hall, New York, 1969; Sov. Radio, Moscow, 1973).
E. S. Levitin and B. T. Polyak, “Constrained Minimization Methods,” Zhurn. Vychisl. Matem. i Matem. Fiz. 6(5), 787–823 (1966).
F. P. Vasil’ev, Numerical Methods for Solving Extremal Problems (Nauka, Moscow, 1988) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © I.Ya. Zabotin and R.S. Yarullin, 2013, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, No. 3, pp. 74–79.
Submitted by Ya.I. Zabotin
About this article
Cite this article
Zabotin, I.Y., Yarullin, R.S. One approach to constructing cutting algorithms with dropping of cutting planes. Russ Math. 57, 60–64 (2013). https://doi.org/10.3103/S1066369X13030092
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X13030092