Mathematical logic in discrete optimization and linear systems, mathematical models of economics.
Main publications:
Davydov G., Davydova I. Dual algorithms in discrete optimization. Amer. Math. Soc. Transl. (2). V. 178. 1996. P. 79–101.
Davydov G., Davydova I. Tautologies and positive solvability of linear homogeneous systems // Ann. Pure Appl. Logic. V. 57. 1992. P. 27–43.
Davydov G. V., Davydova I. M. Number Representations of Satisfiability // J. Math. Sci. A Translation of Selected Russian-Language Serial Publications in Mathematics. V. 98, no. 4. February, 2000. P. 464–477.
Davydov G., Davydova I., Kleine B'uning H. An Efficient Algorithm for the Minimal Unsatisfiability Problem for a Subclass of CNF // Annals of Mathematics and Artifical Intelligence. V. 23. 1998. P. 229–245.
Davydov G., Davydova I. Towards logical operatios research — propositional case // Ann. Pure Appl. Logic. V. 113, no. 1–3. 2001. P. 95–119.
