We investigate a modified version of the previously published method to solve the problem of minimizing a convex functional. This current modification is related to a new procedure for calculating the metric projection included in the step operator of the basic iterative process. Unlike the basic method, its modified version allows to solve the constrained convex minimization problem for compatible and incompatible system of constraints. Numerical experiments confirm the efficiency of both the basic and modified methods.
Keywords: ill-posed and improper problems, convex constraints, iterative process, convex minimization, regularizing algorithm
Received June 24, 2025
Revised October 8, 2025
Accepted October 13, 2025
Funding Agency: The second author’s work was carried out within the framework of the State Assignment of the Sobolev Institute of Mathematics SB RAS (project FWNF-2022-0015).
Vladimir Vasil’evich Vasin, Dr. Phys.-Math. Sci., Corresponding Member of the RAS, Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: vasin@imm.uran.ru
Irina Alekseevna Gainova, Cand. Sci. (Phys.-Math.), Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090 Russia, e-mail: gajnova@math.nsc.ru
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Cite this article as: V.V. Vasin, I.A. Gainova. Constrained convex minimization methods generating regularizing algorithms. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2025, vol. 31, no. 4, pp. 71–84.
