Geodesic
One approach to constructing cutting algorithms with dropping of cutting planes
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2013), pp. 74-79

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We propose a general cutting method for conditional minimization of continuous functions. We calculate iteration points by partially immersing 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.
Keywords: conditional minimization, approximating set, cutting plane, algorithm, sequence of approximations
Mots-clés : convergence. 
@article{IVM_2013_3_a8,
     author = {I. Ya. Zabotin and R. S. Yarullin},
     title = {One approach to constructing cutting algorithms with dropping of cutting planes},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {74--79},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_3_a8/}
}
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I. Ya. Zabotin; R. S. Yarullin. One approach to constructing cutting algorithms with dropping of cutting planes. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2013), pp. 74-79. http://geodesic.mathdoc.fr/item/IVM_2013_3_a8/