01.01.09 (Discrete mathematics and mathematical cybernetics)
Birth date:
06.11.1955
E-mail:
,
Keywords:
theory of utility and decision making; games theory; mathematical programming; mathematical models of economics; mathematical models of operations research; applications of operations research.
Subject:
A notion of exceptional family of elements for finite- and infinite-dimensional complementarity problem was introduced, and theorems of (non-strict) alternative proved. Namely, for the complementarity problem with the upper semicontinuous multi-valued mapping, there exists a solution or an exceptional family of elements. Based upon the theorems of alternative, necessary and sufficient conditions of solvability of the general complementarity problem were obtained. Generalized models of oligopoly with a finite number of non-homogeneous agents were examined, and results of existence and uniqueness of the equilibrium in those models were obtained. For the extended Cournot and Stackelberg models, the quantitative characteristics of the equilibria were compared.
Biography
Graduated from Faculty of Mathematics and Mechanics of M. A. Lavrentiev Novosibirsk State University (NSU) in 1977 (department of mathematical cybernetics). Ph.D. was awarded in 1981. D.Sci. thesis was defended in 1995. A list of my works contains more than 40 titles.
In 1998 I was awarded the prize of the Central Economics and Mathematics Institute (CEMI RAS) for a series of papers on the existence and uniqueness of equilibrium in generalized Cournot and Stackelberg models (jointly with V. A. Bulavsky).
Main publications:
Kalashnikov V. V. and Isac G. Solvability of implicit complementarity problems. Annals of Operations Research, vol. "Operations Research and Systems" (to appear).
Isac G. and Kalashnikov V. V. Exceptional family of elements, Leray-Schauder alternative, pseudomonotone operators and complementarity // J. Optim. Theory Appl., 2001, 109, 69–83.
Bulavsky V. A. and Kalashnikov V. V. A Newton-like approach to solving an equilibrium problem // Annals of Operations Research, 1998, 81, 115–128.
Kalashnikov V. V. and Kalashnikova N. I. Solving two-level variational inequality // J. Global Optimiztion, 1996, 289–294.
Isac G., Bulavsky V. A. and Kalashnikov V. V. Complementarity, Equilibrium, Efficiency, and Economics. Boston: Kluwer Academic Publishers (to appear), 450 pp.
Vyacheslav V. Kalashnikov, Nataliya I. Kalashnykova, Felipe J. Castillo-Pérez, “Consistent conjectural variations equilibrium in an optimal portfolio model”, Contributions to Game Theory and Management, 8 (2015), 99–110
1999
2.
G. Sh. Tsitsiashvili, V. V. Kalashnikov, “Two-Sided Bounds of Random Sums with Subexponential Summands”, Probl. Peredachi Inf., 35:3 (1999), 67–79; Problems Inform. Transmission, 35:3 (1999), 248–258
V. V. Kalashnikov, G. Sh. Tsitsiashvili, “Stability analysis of queueing systems”, Zap. Nauchn. Sem. LOMI, 87 (1979), 41–61; J. Soviet Math., 17:6 (1981), 2238–2255
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