REGULARIZATION OF PARTIALLY INTEGER VECTOR OPTIMIZATION PROBLEMS WITH QUADRATIC CRITERIA
DOI:
https://doi.org/10.15407/dopovidi2024.05.038Keywords:
partially integer problem, Pareto optimization, vector criterion, quadratic functions, perturbations of input data, stability, regularization, set of SlaterAbstract
The article is devoted to the question of regularization of partially integer Pareto-optimization problems with vector criterion input perturbations. New results are obtained for the case when the vector problem is partially integer with quadratic functions as criteria. The developed regularization procedure is based on the use of the Slater stability property with respect to perturbations of criterion coefficients of the vector optimization problem. The obtained results - the conditions of stability to possible perturbations of vector criterion input data and the developed procedure of regularization of vector optimization problems — are related to the solution of problems of correct modeling of economic, ecological, technological, social processes in conditions of effective accounting of incompleteness and uncertainty of input information.
Downloads
References
Sergienko, I. V., Kozeratskaya, L. N. & Lebedeva, Т. Т. (1995). Stability Analysis and Parametric Analysis of Discrete Optimization Problems. Kyiv: Naukova Dumka (in Russian)
Sergienko, I. V. & Shilo, V. P. (2003). Discrete optimization. Problems: challenges, methods, solutions. Kyiv: Naukova Dumka (in Russian)
Emelichev, V. A., Girlich, E., Nikulin, Yu. V. & Podkopaev, D. P. (2002). Stability and regularization of vector problems of integer linear programming. Optimization, 51, No. 4, pp. 645-676. https://doi.org/10.1080/ 0233193021000030760
Lyashko, I. I., Yemelyanov, V. F. & Boyarchuk, O. K. (1992). Mathematical analysis. Part 1. Kyiv: Visha shcola (in Ukrainian)
Lebedeva, Т. Т., Semenova, N. V. & Sergienko, T. I. (2022). Stability and regularization of partially integer problems of vector optimization with possible perturbations of criteria. Dopov. Nac. akad. nauk Ukr., No. 5, pp. 16-22. (in Ukrainian). https://doi.org/10.15407/dopovidi2022.05.016
Lebedeva, Т. Т., Semenova, N. V. & Sergienko, T. I. (2020). Stability by the vector criterion of a mixed integer optimization problem with quadratic criterial functions. Dopov. Nac. akad. nauk Ukr., No. 10, pp. 15-21. (in Ukrainian). https://doi.org/10.15407/dopovidi2020.10.015
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
