Governance/control is one of the most important functions of government. Therefore, automation of control processes based on information computer technology's introduction is an urgent problem of creating an electronic government. The article proposes a methodological approach to the control functions of public authorities' implementation in e-government concept framework. The approach is based on the principle of selective control. The expediency is conditioned upon the impossibility of total control due to limited resources. Optimization of control processes is based on using appropriate models of mathematical programming. The combined application of the selectivity principle and optimization model reduces the state's expenditures for implementation of control functions while ensuring the required quality control. In whole, the methodological approach considered in this paper forms a basis for specific models and methods, formation ensuring the introduction of computer technologies into the control processes of e-government. © IJSTR 2020.