Stability and regularization of partially integer problems of vector optimization with possible perturbations of criteria

Authors

DOI:

https://doi.org/10.15407/dopovidi2022.05.016

Keywords:

vector integer optimization problem, vector criterion, stability, regularization, Pareto-optimal solutions, set of Slater, perturbations of initial data

Abstract

New results related to the study of stability and regularization of partially integer vector optimization problems with possible perturbations of the input data of a vector criterion consisting of quadratic or linear functions are presented. The stability of problems with quadratic criteria for the case of finding solutions that are optimal according to Slater is proved. For the Pareto optimization case, an approach to the regularization of partially integer problems with linear criterion functions is developed.

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References

Kozeratskaya, L. N., Lebedeva, T. T. & Sergienko, T. I. (1991). Mixed integer vector optimization: Stability issues. Cybernetics and Systems Analysis, 27, No. 1, pp. 76-80.

Kozeratskaya, L. N., Lebedeva, T. T. & Sergienko, T. I. (1993). Regularization of integer vector optimization problems, Cybernetics and Systems Analysis, 29, No. 3, pp. 455-458.

Kozeratskaya, L. N. (1994). Vector optimization problems: Stability in the decision space and in the space of alternatives. Cybernetics and Systems Analysis, 30, No. 6, pp. 891-899.

Sergienko, I. V., Kozeratskaya, L. N. & Lebedeva, T. T. (1995). Stability and parametric analysis of discrete optimization problems, Kyiv: Naukova Dumka (in Russian).

Lebedeva, T. T., Semenova, N. V. & Sergienko, T. I. (2005). Stability of vector problems of integer optimization: Relationship with the stability of sets of optimal and nonoptimal solutions. Cybernetics and Systems Analysis, 41, No. 4, pp. 551-558. https://doi.org/10.1007/s10559-005-0090-z

Lebedeva, T. T., Semenova, N. V. & Sergienko, T. I. (2014). Properties of perturbed cones ordering the set of feasible solutions of vector optimization problem. Cybernetics and Systems Analysis, 50, No. 5, pp. 712-714 (in Ukrainian). https://doi.org/10.1007/s10559-014-9661-1

Lebedeva, T. T., Semenova, N. V. & Sergienko, T. I. (2020). Stability by the vector criterion of a mixed integer optimization problem with quadratic criterial functions. Dopov. Nac. acad. nauk Ukr., No. 10, pp. 15-21 (in Ukrainian). https://doi.org/10.15407/dopovidi2020.10.015

Lebedeva, T. T., Semenova, N. V. & Sergienko, T. I. (2020). Multi-Objective Optimization Problem: Stability against Perturbations of Input Data in Vector-Valued Criterion. Cybernetics and Systems Analysis, 56, No. 6, pp. 953-958. https://doi.org/10.1007/s10559-020-00315-9

Lyashko, I. I., Emelyanov, V. F. & Boyarcyuk, O. K. (1992). Mathematical analysis. Part. 1. Kyiv: Visha shcola (in Ukrainian).

Published

28.10.2022

How to Cite

Lebedeva Т. ., Semenova Н. ., & Sergienko Т. . (2022). Stability and regularization of partially integer problems of vector optimization with possible perturbations of criteria. Reports of the National Academy of Sciences of Ukraine, (5), 16–22. https://doi.org/10.15407/dopovidi2022.05.016

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Section

Information Science and Cybernetics

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