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In this paper, a class of multi-extremal stochastic programming problems is considered. Direct and dual problems are also included in this problem, respectively, in this paper the question of the existence of solutions to such problems is studied, the necessary theorems and proofs are given. Decision making under uncertainty is based on the fact that the probabilities of various scenarios are unknown. Decision-making under risk conditions is based on the fact that each situation of the development of events can be...