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<p><i>The paper is concerned with the problem of hard SVM separation of two finite sets in a Euclidean space. It contains a comparative analysis of three related algorithms (Kozinec, MDM, and SMO) used to solve this problem. A unified approach to analysis of these algorithms was made possible due to estimates of plans for the considered extremal problems that have been introduced. An estimate of a plan is always nonnegative. It vanishes if and only if the plan is optimal and a positive estimate allows us to improve the plan. This property serves as a basis for constructing minimizing sequences of plans. The paper proposes working schemes of algorithms that are more efficient than the original (conceptual) schemes. All additional theoretical results required for justification of the results are exposed in ten reports of the “O&amp;ML” seminar and in the bibliographies to these reports. Bibliography: 10 titles.</i></p>

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COMPARATIVE ANALYSIS OF KOZINEC, MDM AND SMO ALGORITHMS FOR SOLVING THE HARD SVM SEPARATION PROBLEM

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • V. N. Malozemov,
  • G. Sh. Tamasyan

摘要

The paper is concerned with the problem of hard SVM separation of two finite sets in a Euclidean space. It contains a comparative analysis of three related algorithms (Kozinec, MDM, and SMO) used to solve this problem. A unified approach to analysis of these algorithms was made possible due to estimates of plans for the considered extremal problems that have been introduced. An estimate of a plan is always nonnegative. It vanishes if and only if the plan is optimal and a positive estimate allows us to improve the plan. This property serves as a basis for constructing minimizing sequences of plans. The paper proposes working schemes of algorithms that are more efficient than the original (conceptual) schemes. All additional theoretical results required for justification of the results are exposed in ten reports of the “O&ML” seminar and in the bibliographies to these reports. Bibliography: 10 titles.