SUMMARY
Context. The problem of justifying methods for constructing models of optimization procedures as dynamic objects, taking into account the features of the training procedures, is considered. The object of the study were models of the dynamics of training procedures.Objective. The goal of the work is to solve the tasks of formalizing the training procedures, developing methods for constructing mathematical models of the learning processes, the processes of searching for the optimum of the learning tasks, and for evaluating dynamic training procedures.Method. The learning process is a totality of sequential and interrelated actions of a teacher and learners, aimed at providing a conscious and durable assimilation of knowledge, abilities, and skills. As a result of systematic analysis, main, basic patterns of training procedures are defined. The notion of “information flow” is justified as the sequence of messages carrying information for building models of interactions in information systems. The important property of the information flow is determined – the directionfrom the source to the receiver. Two possible variants of information interaction of objects are singled out – information transfer and information compensation. The use of optimality principle for information processes of learning is offered. It is shown that the dynamics of learning processes is determined by the characteristics of the used optimization procedure. The gradient procedure for finding the extremum of the goal function is described by the autonomous motion of the dynamic system. For a strictly convex goalfunction, according to sufficient optimality conditions, the optimization procedure is described by the dynamics of the autonomous motion of a stationary linear unbound dynamic object. The choice of the multiplier for the gradient significantly affects the dynamics of the process, and for a strictly convex goal function the multiplier is equal to the increment vector. The use of a dynamic model determines the number of steps required to achieve the given accuracy.Results. The created models received software implementation and were investigated in practice when solving the tasks of modeling the dynamics of training procedures in the teaching process of the Information Technologies Department of Kherson National Technical University.Conclusions. The carried out experimental researches have allowed to confirm practically operability of the created mathematical apparatus and to consider it expedient for application with the purpose of increase of efficiency of modeling and realization of training procedures. Further perspectives of the research are seen in the coverage of more types of dynamic training procedures, optimizing approaches to their software implementations, and increasing the scale of their coverage with confirmatory experiments.