Nonlocal quasi-Newton method for solving convex variational inequalities

Conclusion In the optimization problem [f ₀(x)│h_i(x)<-0,i=1,…,l] relaxation of the functionf ₀(x)+Nh⁺(x) does not produce, as we know [6, 7], α_k=1 in Newton's method with the auxiliary problem (5), (6), whereF(x)=f _0′(x). For this reason, Newton type methods based on relaxation off ₀(x)+Nh⁺(x) are not superlinearly convergent (so-called Maratos effect). The results of this article indicate that if (F(x)=f _0′(x), then replacement of the initial optimization problem with a larger equivalent problem (7) eliminates the Maratos effect in the proposed quasi-Newton method. This result is mainly of theoretical interest, because Newton type optimization methods in the space of the variablesx ∈R ⁿ are less complex. However to the best of our knowledge, the difficulties with nonlocal convergence arising in these methods (choice of parameters, etc.) have not been fully resolved [10, 11]. The discussion of these difficulties and comparison with the proposed method fall outside the scope of the present article, which focuses on solution of variational inequalities (1), (2) for the general caseF′(x)≠F′ ^T(x). Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 78–91, November–December, 1994.     

Large-deviation inequalities for parameter estimators in stochastic systems

Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 95–112, March–April, 1994.     

Fault trees—Problems and the modern state of investigations

Published in Kibernetika i Sistemnyi Analiz, No. 3, pp. 128–150, May–June, 1994.     

Some features of the chemical transformation of a highly exothermic ore concentrate-based mixture in a combustion wave

Use of inexpensive ore concentrates as initial components in SHS metallurgy [1–3] brings about some specific features in the process and the properties of the materials obtained. Ore reagents contain a considerable amount of impurities (Al₂O₃, SiO₂, Fe₂O₃) that decrease the energetics of SHS systems and the temperature and the rate of combustion and create the limits of combustion and phase separation. In addition, the impurities participate in chemical reactions and enter the desired product. In many cases the presence of silicon, iron, and aluminum in a cast product does not prevent use of this product for practical purposes.Institute of Metallurgy, Academy of Sciences of the Republic of Georgia, Tbilisi. Institute of Structural Macrokinetics, Russian Academy of Sciences, Chernogolovka. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 5, pp. 613–616, November, 1993.