Comparative analysis of Kozinec, MDM and SMO algorithms for solving the hard SVM separation problem

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.