• Linearization, reduced gradient, modified Lagrange function. Theorems of alternative linear inequality systems. Symmetrical duality in optimization. Application to the models of electric and pipeline systems;
  
• Formation of a theory and methods for solution of global optimization and equilibrium pro-gramming problems, methods of two-level programming;
  
• Study on the problems of coordinating interests and the multi-objective problems as applied to energy. Numerical methods for determination of Nash and Pareto optimal solutions. Theory and methods of decision making under conditions of uncertainty. Development of combinatorial modeling methods to study the options of energy systems development;
  
• Study of aggregation problems in economics. Theory and methods of formation of economic indexes, modeling of macroeconomic processes. Software for construction and analysis of dynamic models of energy, economic and ecological systems;
  
• Development of a theory and numerical methods of solving non-classical integral equations of Volterra of the first kind. Development of fundamentals of the theory on multilinear equations of Volterra type. Obtaining the optimal estimates of solutions to nonlinear integral inequalities with isotonic operators in K-spaces;
  
• Methods for identification of nonlinear dynamic systems modeled by Volterra polynomials, and their application in heat power industry. Construction of integral models of dynamically devel-oping systems as applied to the problem of long-term expansion of generation capacities in electric power industry.

In recent years the department staff actively particpate in the fundamental research projects under grants of Russian Foundation of Basic Research, Russian Humanitarian Scientific Foundation and others.