Speciality:
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.
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.
