The paper proposes an approach based on gradient-free stochastic convex optimization with an inexact oracle of zero-order to solve a special case of the dynamic pricing problem with a variable flow of customers when the training data contains information about purchases made, but the number of refusals to purchase at the given price is unknown. The paper considers a model with one customer segment and one type of product as a possible element of more complex, hierarchical dynamic pricing models. In the unavailability of data on rejections for reduction to a convex non-gradient optimization problem, the work uses the technique of logarithmization of the objective function and random division of the customer segment into two subsegments at each iteration.