CHIZIQLI PROGRAMMALASHTIRISH MASALALARINING GEOMETRIK TALQINI VA OPTIMAL YECHIMLARINI TADQIQ ETISH
Keywords:
Kalit so‘zlar: chiziqli programmalashtirish, geometrik usul, ruxsat etilgan soha, optimal yechim, burchak nuqta, simpleks usuli, iqtisodiy model, optimallashtirish, konveks ko‘pburchak.Abstract
ANNOTATSIYA
Annotatsiya. Mazkur maqolada chiziqli programmalashtirish masalalarining
geometrik talqini, ruxsat etilgan yechimlar sohasi, ekstremal nuqtalar va optimal
yechimlar tushunchalari tizimli ravishda tahlil qilindi. Tadqiqotning nazariy qismida
maqsad funksiyasi va cheklovlar tizimi orqali iqtisodiy-matematik model qurish
tamoyillari, burchak nuqtalar teoremasining mazmuni hamda simpleks usulining
geometrik usul bilan bog‘liqligi yoritildi. Amaliy qismda ikki o‘zgaruvchili chiziqli
programmalashtirish masalasi tanlanib, koordinata o‘qlari, cheklovlar chiziqlari va
ruxsat etilgan soha aniqlandi. Barcha burchak nuqtalar hisoblanib, maqsad funksiyasi
qiymatlari solishtirildi. Natijada optimal yechim (x₁, x₂) = (20, 60) va optimal qiymat
Z = 2600 ekani ko‘rsatildi. Maqola geometrik usulning didaktik va amaliy afzalliklarini
hamda uning katta o‘lchamli masalalarda simpleks va ichki nuqta usullariga o‘tish
uchun nazariy poydevor bo‘lib xizmat qilishini asoslaydi.
References
ADABIYOTLAR
1. Dantzig, G. B., & Thapa, M. N. (1997). Linear programming 1: Introduction.
Springer.
2. Eiselt, H. A., & Sandblom, C.-L. (2007). Linear programming and its
applications. Springer.
3. Hillier, F. S., & Lieberman, G. J. (2021). Introduction to operations research
(11th ed.). McGraw-Hill Education.
4. Vanderbei, R. J. (2020). Linear programming: Foundations and extensions (5th
ed.). Springer.
5. Golden, B., Schrage, L., Shier, D., & Apergi, L. A. (2024). The unexpected
power of linear programming: An updated collection of surprising applications. Annals
of Operations Research, 343, 573–605.
6. Gondzio, J. (2025). Interior point methods in the year 2025. EURO Journal on
Computational Optimization, 13, 100105.
7. Cococcioni, M., & Fiaschi, L. (2025). Linear programming with infinite, finite,
and infinitesimal values in the right-hand side. Applied Mathematics and Computation,
129044.
8. Cole, R., et al. (2025). A first order method for linear programming
parameterized by the circuit imbalance measure. Mathematical Programming.
9. Im, H., et al. (2023). Revisiting degeneracy, strict feasibility, stability, in linear
programming. European Journal of Operational Research, 310(2), 1–15.
10. Chernov, V. (2024). Conditions when the problems of linear programming are
decidable by the simplex method. Algebra and Logic, 63(5), 293.
11. Sinuany-Stern, Z., et al. (2023). Foundations of operations research: From
linear programming to DEA. European Journal of Operational Research.
12. Hladík, M. (2025). Interval linear programming and extensions. Springer.
13. Saipnazarov, M. (2022). Biznes matematika. Innovatsion rivojlanish nashriyot-
matbaa uyi.
