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On volumes of bounded convex sets

For the n-dimensional golden search method used to solve a constrained optimization problem with a bounded closed convex feasible set X in the n-dimensional Euclidean space, one can evaluate the number of computations of the objective values. This evaluation requires, however, a search for a lower bound for the volume of X which is based on elementary geometrical facts. In this connection, one can observe that the closedness condition with respect to X need not be assumed. If we apply the obtained results to an n-simplex S for which every vertex has distance h to the being opposite bounding hyperplane, then S turns out to be a bounded convex set with minimal volume.