Registration Number
0225U000370,
(0123U103184)
, R & D reports
Title
To develop non-smooth optimization algorithms for clustering and statistical data processing
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Розробити методи негладкої оптимізації для задач кластеризації та задач статистичної обробки результатів спостережень
Head
Stovba Viktor O., Доктор філософії
Registration Date
10-01-2025
Organization
V.M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine
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The goal of scientific research is the development of models and methods of non-smooth optimization for solving problems of clustering and statistical processing of observation data.
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Investigated in the paper is storage location problem, substantiated consistency conditions of constraint system of the problem, considered its variants depending on the balance conditions that determine degeneracy and non-degeneracy of constraint system. For finding parameters of linear regression model with L1-regularization and criterion of sum of residuals moduli powered to p∈[1,2], the emlmpr algorithm is constructed. Test experiments results demonstrate program running time, robustness of solutions of the problem at p≈1, and quality of model parameters restoration if there is a linear dependence between the factors. A Boolean linear programming model is formulated for classification problem and method for calculating lower estimates of model's objective function based on non-smooth dual problem obtained via Lagrangian relaxation of some constraints of the initial problem is described. A Feyer-type supergradient algorithm is constructed for its solution. Experiments results using the dual approach are presented and compared with Gurobi and kmeans++ results. Problem of finding lower bound of the Gutman reliability coefficient for educational testing problem and related nonlinear programming problem, formulated as linear function maximizing problem under non-smooth constraints on minimum eigenvalue of symmetric matrix, which is reduced to unconditional maximization of a non-smooth function, are investigated. Test case is constructed for its solution using r-algorithm, and results obtained are compared with Fletcher's ones. For the model of a two-stage transportation problem with constraints on unknown consumer demands, necessary and sufficient conditions for constraint system consistency are substantiated. A partial case of the original problem is formulated, when the lower and upper bounds on consumer needs coincide, and its modification, in which some consumers are removed from transportation plan, and products are transported only to fixed number of consumers.
Product Description
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Korablov Mykola M.
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2025-01-10
