Registration Number
0222U000966,
0119U101608
, R & D reports
Title
New methods for wellposedness investigation and solving of discrete optimization problems, variational inequalities and their applications
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Head
Serhiienko Ivan V., Доктор фізико-математичних наук
Registration Date
22-01-2022
Organization
Department for special training National academy of science of Ukraine at Kiev University
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The conditions of existence and optimality of solutions of vector lexicographic optimization problems are established. For a vector optimization problem with continuous criterion functions and a set of feasible solutions of an arbitrary structure, the conditions of stability with respect to perturbations of the input data of the vector criterion are determined. A two-stage Bregman method of extrapolation from the past with an adaptive rule of step size selection is proposed. A new operator extrapolation algorithm with Bregman projection and generalized Alber projection is proposed to solve variational inequalities in Hilbert and uniformly convex Banach spaces. A new algorithm is proposed to solve two-level monotone variational inequalities. The weak convergence of the two-stage proximal algorithm for equilibrium problems in Hilbert space is proved. Under the condition of sharp equilibrium, finite convergence is proved. New adaptive two-stage proximal algorithms for equilibrium problems in Hadamard metric spaces are proposed.
Product Description
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Lebedeva Tetiana T.
Lyashko Sergiy I.
Semenova Nataliia V.
Sergienko Ivan V.
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2022-03-09
