Geodesic
A cutting-plane method with internal iteration points for the general convex programming problem
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 165 (2023) no. 3, pp. 208-218

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A cutting method for solving the problem of convex programming was proposed. The method calculates iteration points based on approximation by polyhedral sets of the constraint region and the epigraph of the objective function. Its distinguishing feature is that the main sequence of approximations is constructed within the admissible region. At each step, it is also possible to assess how close the current value of the function is to the optimal value. The convergence of the method was proved. A few of its implementations were outlined.
Keywords: convex programming, conditional minimization, set approximation, function epigraph, iteration point, sequence of approximations, cutting hyperplane
Mots-clés : optimal value, convergence. 
@article{UZKU_2023_165_3_a2,
     author = {I. Ya. Zabotin and K. E. Kazaeva and O. N. Shul'gina},
     title = {A cutting-plane method with internal iteration points for the general convex programming problem},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {208--218},
     publisher = {mathdoc},
     volume = {165},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2023_165_3_a2/}
}
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I. Ya. Zabotin; K. E. Kazaeva; O. N. Shul'gina. A cutting-plane method with internal iteration points for the general convex programming problem. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 165 (2023) no. 3, pp. 208-218. http://geodesic.mathdoc.fr/item/UZKU_2023_165_3_a2/