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Статья
2013

One approach to constructing cutting algorithms with dropping of cutting planes


I. Ya. ZabotinI. Ya. Zabotin, R. S. YarullinR. S. Yarullin
Русская математика
https://doi.org/10.3103/S1066369X13030092
Abstract / Full Text

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.

Author information
  • Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, RussiaI. Ya. Zabotin & R. S. Yarullin
References
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  2. I. Ya. Zabotin, “Some Embedding-Cutting Algorithms for Mathematical Programming Problems,” Izv. Irkutsk. Gos. Univ., Ser. Matem. 4(2), 91–101 (2011).
  3. U. I. Zangwill, Nonlinear Programming: A Unified Approach (Prentice-Hall, New York, 1969; Sov. Radio, Moscow, 1973).
  4. E. S. Levitin and B. T. Polyak, “Constrained Minimization Methods,” Zhurn. Vychisl. Matem. i Matem. Fiz. 6(5), 787–823 (1966).
  5. F. P. Vasil’ev, Numerical Methods for Solving Extremal Problems (Nauka, Moscow, 1988) [in Russian].