УДК 330.115

Ю. Єрмольєв,
Міжнародний Інститут прикладного системного аналізу, Лаксенбург, Австрія,
 ermoliev@iiasa.ac.at

А. Загородній,
Інститут теоретичної фізики ім. Боголюбова НАН України, Київ, Україна,
 Zagorodny@nas.gov.ua

В. Богданов,
Інститут механіки імені С.П. Тимошенка НАН України, Київ, Ураїна,
 Bogdanov@nas.gov.ua

Т. Єрмольєва,
Міжнародний Інститут прикладного системного аналізу, Лаксенбург, Австрія,
 ermol@iiasa.ac.at

П. Гавлік,
Міжнародний Інститут прикладного системного аналізу, Лаксенбург, Австрія,
 havlipt@iiasa.ac.at

О. Ровенська,
Міжнародний Інститут прикладного системного аналізу, Лаксенбург, Австрія,
 rovenska@iiasa.ac.at

Н. Комендантова,
Міжнародний Інститут прикладного системного аналізу, Лаксенбург, Австрія,
 komendan@iiasa.ac.at

М. Оберштайнер,
Міжнародний Інститут прикладного системного аналізу, Лаксенбург, Австрія,
 oberstei@iiasa.ac.at

РОБАСТНЕ УПРАВЛІННЯ ДЛЯ БЕЗПЕКИ У ВЗАЄМОЗАЛЕЖНІЙ СИСТЕМІ
ПРОДОВОЛЬСТВО–ЕНЕРГІЯ–ВОДА–ДОВКІЛЛЯ: ПРОЦЕДУРА
СТОХАСТИЧНИХ КВАЗІГРАДІЄНТІВ ДЛЯ ЗВ’ЯЗУВАННЯ РОЗПОДІЛЕНИХ
ОПТИМІЗАЦІЙНИХ МОДЕЛЕЙ В УМОВАХ АСИМЕТРИЧНОЇ ІНФОРМАЦІІ
ТА НЕВИЗНАЧЕНОСТІ

ПОВНИЙ ТЕКСТ

СПИСОК ЛІТЕРАТУРИ

1. Ermoliev Y. Stochastic quasigradient methods in minimax problems. In: Encyclopedia of Optimization. Floudas C.A., Pardalos P.M. (Eds.). New York: Springer-Verlag, 2009. P. 3813–3818.


2. Ermoliev Y. Two-stage stochastic programming: quasigradient method. In: Encyclopedia of Optimization. Floudas C.A., Pardalos P.M. (Eds.). New York: Springer-Verlag, 2009. P. 3955–3959.


3. Ermoliev Y. Stochastic quasigradient methods: applications. In: Encyclopedia of Optimization. Floudas C.A., Pardalos P.M. (Eds.). New York: Springer-Verlag, 2009. P. 3807–3813.


4. Ermoliev Y. Stochastic quasigradient methods. In: Encyclopedia of Optimization. Floudas C.A., Pardalos P.M. (Eds.). New York: Springer-Verlag, 2009. P. 3801–3807.


5. Ermoliev Y., Norkin V. On nonsmooth and discontinuous problems of stochastic systems optimization. European Journal of Operational Research. 1997. Vol. 101, Iss. 2. P. 230–244. https://doi.org/10.1016/S0377-2217(96)00395-5.


6. Ermolieva T., Ermoliev Y., Rovenskaya E., Obersteiner M. Two-stage nonsmooth stochastic optimization and iterative stochastic quasigradient procedures for robust estimation, machine learning and decision making. In: Resilience in the Digital Age. Roberts F.S., Sheremet I. (Eds.). Springer International Publishing, 2021. P. 45–74.


7. Food-Energy-Water NEXUS for Sustainable Development: Integrated Modeling and Robust management. Zagorodny A.G., Ermoliev Yu.M., Bogdanov V.L., Ermolieva T. (Eds.). Kyiv: PH “Akademperiodyka”. 2020. 446 p. URL: https://ru.calameo.com/read/0031683726252f5034d74.


8. Zagorodny A.G., Ermoliev Y., Bogdanov V.L., Kostyuchenko Y.V., Ermolieva. T. Integrated robust management of food-energy-water-land use nexus for sustainable development. In: Food-Energy-Water NEXUS for Sustainable Development: Integrated Modeling and Robust management. Zagorodny A.G., Ermoliev Yu.M., Bogdanov V.L., Ermolieva T. (Eds.). Kyiv: PH “Akademperiodyka”, 2020. P. 237–250.


9. Ermoliev Y., Zagorodny A.G., Bogdanov V.L., Ermolieva T., Havlik P., Obersteiner M., Rovenskaya E. Linking distributed sectorial and regional optimization models under asymmetric information: towards robust food-water-energy-environmental nexus. In: Food-Energy-Water NEXUS for Sustainable Development: Integrated Modeling and Robust management. Zagorodny A.G., Ermoliev Yu.M., Bogdanov V.L., Ermolieva T. (Eds.). Kyiv: PH “Akademperiodyka”, 2020. P. 303–323.


10. Ermoliev Y., Zagorodny A.G., Bogdanov V.L., Knopov P.S., Borodina O.M., Ermolieva T., Rovenskaya E., Kostjuchenk Y.V., et al. Integrated robust management of NEXUS between agricultural, water, energy economic sectors: consistent algorithms for linking distributed models. Proc. 6th International Conference on Mathematical Modeling, Optimization and Information Technologies (12–16 November, 2018, Kischinev, Moldova). Kischinev, 2018. P. 108–112.


11. Gao J., Xu X., Cao G., Ermoliev Y.M., Ermolieva T.Y., Rovenskaya E.A. Optimizing regional food and energy. Sustainability. 2018. Vol. 10, Iss. 6. 1689. https://doi.org/10.3390/su10061689.


12. Ermoliev Y. Production under limited water availability through integrated modeling. Some problems of linkage systems. IIASA Working Paper WP-80-102. Laxenburg, Austria: Int. Institute for Applied Systems Analysis (IIASA), 1980. 15 p. URL: http://pure.iiasa.ac.at/id/eprint/1367/1/WP-80-102.pdf.


13. Arrow K.J. Studies in linear and nonlinear programming. Stanford, CA: Stanford University Press, 1958. 229 p.


14. Bertsekas D. Nonlinear programming. Belmont: Atlanta Scientific, 1999. 791 p.


15. Ermoliev Y. Methods of stochastic programming. Moscow: Nauka, 1976. 240 p. (In Russian).


16. Rockafeller R.T. The theory of subgradient and its application to problems of optimization: convex and nonconvex functions. Berlin: Helderman Verlag, 1981. 107 p.


17. Ermoliev Y., Robinson S., Rovenskaya E., Ermolieva T. Integrated catastrophic risk management: Robust balance between Ex-ante and Ex-post measures. SIAM News. 2018. Vol. 51, Iss. 6. P. 4.


18. Ermoliev Y., Ermolieva T., MacDonald G., Norkin V. Stochastic optimization of insurance portfolios for managing exposure to catastrophic risks. Annals of Operations Research. 2000. Vol. 99, Iss. 1. P. 207–225.


19. Ermolieva T., Ermoliev Y., Fischer G., Galambos I. The role of financial instruments in integrated catastrophic flood management. Multinational Finance Journal. 2003. Vol. 7, Iss. 3–4. P. 207–230.


20. Ermoliev Y., von Winterfeldt D. Systemic risk and security management. In: Managing safety of heterogeneous systems: Decisions under uncertainty and risks. Ermoliev Y., Makowski M., Marti K. (Eds.). New York: Springer, 2012. P. 19–49. URL: link.springer.com/chapter/10.1007/ 978-3-642-22884-1_2.


21. Ermolieva T., Ermoliev Y. Catastrophic risk management: flood and seismic risk case studies. In: Applications of Stochastic Programming. MOS-SIAM Series on Optimization. Wallace S.W., Ziemba W.T. (Eds.). 2005. P. 425–444.


22. Ermoliev Y., Gaivoronski A. Stochastic quasigradient methods for optimization of discrete event systems. Annals of Operations Research. 1992. Vol. 39, Iss. 1. P. 1–39. URL: https://link.springer.com/article/10.1007%2FBF02060934.


23. Gaivoronski A. Convergence properties of backpropagation for neural nets via theory of stochastic guasigradient methods. Part 1. Optimization Methods and Software. 1994. Vol. 4, Iss. 2. P. 117–134.


24. Ermoliev Y., Michalevich M., Uteuliev N.U. Economic modeling of international water use (The case of the Aral Sea Basin). Cybernetics and Systems Analysis. 1994. Vol. 30, N 4. P. 523–527. https://doi.org/10.1007/BF02366562.


25. Ermoliev Y., Wets R.J-B. Numerical techniques for stochastic optimization. Heidelberg: Springer-Verlag, 1988. XV, 571 p.


26. Dantzig G.B., Wolfe P. The decomposition principle for linear programming. Econometrica. 1961. Vol. 29, N 4. P. 767–778.


27. Kim K., Nazareth J.L. The decomposition principle and algorithms for linear programming. Linear Algebra and Its Applications. 1991. Vol. 152. P. 119–133.