Constrained convex minimization methods generating regularizing algorithms

V. V. Vasin^a, I. A. Gainova<sup>b

a</sup> N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: 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.

UDC: 517.988

MSC: 65J20, 65K05

Received: 26.06.2025
Revised: 08.10.2025
Accepted: 13.10.2025

DOI: 10.21538/0134-4889-2025-31-4-71-84

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