Hlebena M. Mathematical models and numerical methods of majorant type for analysis of discrete optimization processes.

The thesis is devoted to the construction and argumentation of new numerical methods for finding the absolute zero order extremum for logarithmically concave, non-smooth and discontinuous functions of one, two or several real variables for the analysis of models of discrete optimization processes (model of optimal information access database files, model analysis of information processing). In the thesis a model of optimal information access database files and model analysis of information processing are being realized. Methods of finding the absolute extremum as arbitrary logarithmically concave and arbitrary non-smooth or discontinuous functions of one real variable, based on the use of the apparatus of non-classical majorants and Newton diagrams of functions of one real variable defined tabular. Methods of finding the absolute extremum as arbitrary logarithmically concave and arbitrary non-smooth and discontinuous functions of two real variables, which are based on the use of the apparatus of non-classical majorants and Newton diagrams of functions of two real variables defined tabular. There were found the absolute extremum logarithmically concave arbitrary functions of many variables algorithm method type of coordinate lifting, which are based on the use of the apparatus of non-classical majorants and Newton diagrams of functions of one real variable defined tabular. There are found the estimates for the number of steps in the case of finding the absolute extremum of a given accuracy of concave logarithmic functions of one, two or many variables. These methods are convergent for any initial approximation and obtain a solution accurate to step value and are effective in solving multiextremum problems.