Geodesic
A cutting plane algorithm with an approximation of an epigraph
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 4, pp. 48-54

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For the conditional minimization problem, we propose a cutting plane algorithm with an approximation of the epigraph of the objective function. The algorithm makes it possible to update approximating sets by dropping the cutting planes which accumulate during the solution process. We prove the convergence of the algorithm and describe its properties.
Keywords: approximating set, cutting hyperplane, sequence of approximations, conditional minimization, epigraph.
Mots-clés : convergence 
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     author = {I. Ya. Zabotin and R. S. Yarullin},
     title = {A cutting plane algorithm with an approximation of an epigraph},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {48--54},
     publisher = {mathdoc},
     volume = {155},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2013_155_4_a4/}
}
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I. Ya. Zabotin; R. S. Yarullin. A cutting plane algorithm with an approximation of an epigraph. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 4, pp. 48-54. http://geodesic.mathdoc.fr/item/UZKU_2013_155_4_a4/