Geodesic
A Cutting-Plane Method with Updating of Approximating Sets and Estimates of the Solution Accuracy
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 2, pp. 54-64

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We propose a cutting-plane method for solving a mathematical programming problem. A sequence of approximations is constructed using the technique of partial immersion of the admissible set in the approximating polyhedral sets. The developed method does not require the inclusion of each of the approximating sets in the previous one. This peculiarity makes it possible to periodically drop any additional planes which occur in the problem-solving process. We describe the features of the method, prove its convergence, and obtain estimates of the solution accuracy.
Keywords: approximating set, cutting plane, estimates of solution accuracy, sequence of approximations, conditional minimization.
Mots-clés : convergence 
@article{UZKU_2013_155_2_a4,
     author = {I. Ya. Zabotin and R. S. Yarullin},
     title = {A {Cutting-Plane} {Method} with {Updating} of {Approximating} {Sets} and {Estimates} of the {Solution} {Accuracy}},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {54--64},
     publisher = {mathdoc},
     volume = {155},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2013_155_2_a4/}
}
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I. Ya. Zabotin; R. S. Yarullin. A Cutting-Plane Method with Updating of Approximating Sets and Estimates of the Solution Accuracy. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 2, pp. 54-64. http://geodesic.mathdoc.fr/item/UZKU_2013_155_2_a4/