We describe the minimum volume simplex enclosure problem (MVSEP), which is known to be a global optimization problem, and further investigate its multimodality. The problem is a basis for several (unmixing) methods that estimate so-called endmembers and fractional values in a linear mixing model. We describe one of the estimation methods based on MVSEP. We show numerically that using nonlinear optimization local search leads to the estimation results aimed at. This is done using examples, designing instances and comparing the outcomes with a maximum volume enclosing simplex approach which is used frequently in unmixing data.