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The subject matter of the article is a discrete dynamic system that consists of an object whose dynamics is described by a vector linear discrete recurrent relation and is affected by control parameters (managements) and uncontrolled parameters (the vector of risks or interference). It is supposed that the phase conditions of the object, management actions and the vector of risks of the considered dynamic system at any moment of time are constrained by given finite or convex polyhedral sets in corresponding finite-dimensional vector spaces. The objective of the article is to model a task of adaptive management of an enterprise innovative processes (EIP) under risks, which requires to complete the following tasks: to develop a software model of managing EIP under risks; to formalize the task of optimizing the EIP adaptive management and general paradigm of its solving as a guaranteed result based on minimax (optimizing a guaranteed result at a given final moment of time considering risks). In such a case, risks in the system of EIP management are thought of as factors that negatively or even catastrophically affect the results of the processes considered in it. In view of this, it is suggested to use the deterministic approach based of the methods of the theory of optimal management and dynamic optimization. The result of the research is a recurrent algorithm which reduces the initial multi-step task to the implementation of finite sequence of tasks of minimax software management of EIP. In turn, the implementation of each task is reduced to the implementation of finite sequence of only one-step optimizing operations as the tasks of linear convex mathematical and discrete optimization. The following conclusions are made: the suggested method makes it possible to work out efficient numerical procedures that enable computer modelling the dynamics of the target task, developing adaptive minimax management of EIP and obtaining an optimal guaranteed result. The results demonstrated in the work can be used for economic and mathematical modelling and solving other tasks of optimizing processes of data prediction and management under the lack of information and under risks as well as for developing corresponding software and hardware complexes to support efficient managerial decisions in practice.

THE TASK OF MINIMAX ADAPTIVE MANAGEMENT OF INNOVATIVE PROCESSES AT AN ENTERPRISE WITH RISK ASSESSMENT