Geodesic
Comparative analysis of Kozinec, MDM and SMO algorithms for solving the hard SVM separation problem
Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part III, Tome 539 (2024), pp. 102-119 
V. N. Malozemov; G. Sh. Tamasyan. Comparative analysis of Kozinec, MDM and SMO algorithms for solving the hard SVM separation problem. Zapiski Nauchnykh Seminarov POMI, Investigations on applied mathematics and informatics. Part III, Tome 539 (2024), pp. 102-119. http://geodesic.mathdoc.fr/item/ZNSL_2024_539_a5/
@article{ZNSL_2024_539_a5,
     author = {V. N. Malozemov and G. Sh. Tamasyan},
     title = {Comparative analysis of {Kozinec,} {MDM} and {SMO} algorithms for solving the hard {SVM} separation problem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {102--119},
     year = {2024},
     volume = {539},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_539_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper provides a comparative analysis of three related algorithms for solving the problem of hard SVM separation of two finite sets in a Euclidean space. These algorithms are the Kozinec, MDM, and SMO algorithms. It is possible to elaborate a unified approach to the analysis of these algorithms due to the fact that “estimates of plans” for the considered extremal problems have been introduced. The estimate of a plan is always non-negative, and it vanishes if and only if the plan is optimal. A positive estimate allows us to improve the plan. This serves as a basis for constructing a minimizing sequence of plans. The paper proposes and compares “working” schemes of algorithms that are more efficient than the original (principal) schemes. All the necessary theoretical results were presented in ten reports of the “O&ML” seminar and in the bibliographies to these reports.

[1] V. N. Malozemov, A. V. Plotkin, “SVM-metod strogogo lineinogo otdeleniya dvukh konechnykh mnozhestv”, Seminar “O”. Izbrannye doklady (30 marta 2022 g.) http://oml.cmlaboratory.com/reps22.shtml#0330

[2] V. N. Malozemov, A. V. Plotkin, “SVM-metod: myagkoe otdelenie”, Seminar “O”. Izbrannye doklady (6 aprelya 2022 g.) http://oml.cmlaboratory.com/reps22.shtml#0406

[3] V. N. Malozemov, A. V. Plotkin, “Strogoe lineinoe otdelenie dvukh konechnykh mnozhestv i lineinoe programmirovanie”, Seminar “O”. Izbrannye doklady (24 fevralya 2022 g.) http://oml.cmlaboratory.com/reps22.shtml#0224

[4] V. N. Malozemov, N. A. Soloveva, G. Sh. Tamasyan, “Ob algoritme Kozintsa. I”, Seminar “O”. Izbrannye doklady (14 marta 2024 g.) http://oml.cmlaboratory.com/reps24.shtml#0314

[5] V. N. Malozemov, N. A. Soloveva, G. Sh. Tamasyan, “Ob algoritme Kozintsa. II”, Seminar “”. Izbrannye doklady (21 marta 2024 g.) http://oml.cmlaboratory.com/reps24.shtml#0321

[6] V. N. Malozemov, N. A. Soloveva, “Obschaya kvadratichnaya zadacha matematicheskoi diagnostiki”, Seminar “O”. Izbrannye doklady (11 maya 2022 g.) http://oml.cmlaboratory.com/reps22.shtml#0511

[7] V. N. Malozemov, N. A. Soloveva, “MDM-metod dlya resheniya obschei kvadratichnoi zadachi matematicheskoi diagnostiki”, Seminar “O”. Izbrannye doklady (1 iyunya 2022 g.) http://oml.cmlaboratory.com/reps22.shtml#0601

[8] V. N. Malozemov, N. A. Soloveva, “SMO-algoritm kak obobschenie MDM-algoritma”, Seminar “O”. Izbrannye doklady (16 fevralya 2023 g.) http://oml.cmlaboratory.com/reps23.shtml#0216

[9] V. N. Malozemov, N. A. Soloveva, “Kartina maslom”, Seminar “O”. Izbrannye doklady (11 maya 2023 g.) http://oml.cmlaboratory.com/reps23.shtml#0511

[10] V. N. Malozemov, N. A. Soloveva, “Silnaya skhodimost SMO-algoritma”, Seminar “O”. Izbrannye doklady (30 noyabrya 2023 g.) http://oml.cmlaboratory.com/reps23.shtml#1130