Iterative methods for large-scale problems

Gamidov, Rafael H.; Mutallimov, Mutallim M.

doi:10.22034/cmde.2025.67389.3208

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	Iterative methods for large-scale problems
Computational Methods for Differential Equations
مقاله 28، دوره 14، شماره 1، فروردین 2026، صفحه 411-420 اصل مقاله (377.23 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.67389.3208
نویسندگان
Rafael H. Gamidov¹؛ Mutallim M. Mutallimov^* ²
¹Baku State University, Baku, Azerbaijan.
²1. Institute of Applied Mathematics, BSU, Baku, Azerbaijan. \\ 2. Institute of Information Technology, Ministry of Science and Education of the Republic of Azerbaijan, Baku, Azerbaijan.\\ 3. Azerbaijan Technical University, Baku, Azerbaijan.
چکیده
One linear bi-criterion mathematical program, which appears as a large-scale problem in practice, is considered. Problems related to the large size are usually solved with the help of methods based on the possibilities created by the zeros of the matrix of the problem. In this way, a large number of different separation schemes have been suggested in the scientific literature. However, the problems considered here have no such possibility due to their large size. In order to overcome the size problem during the solution of the problem, the possibility of reducing it to a smaller problem is investigated. The reduction is carried out without disturbing the original structure of the problem. The goal is to maintain the possibility of using the existing effective solution methods for the problems before the reduction, as well as for the problems received after the reduction. Suggested here method mainly uses sequential approximation schemes to fulfill.
کلیدواژه‌ها
Linear programming؛ Dual problem؛ Dual theorem؛ Basic variable؛ Basic solution؛ Pareto bound

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Iterative methods for large-scale problems