Thank you both! I tested both approaches and they work, complying with my purpose -to have an element greater than or equal to 0.05 in the simplex-.
However, this has lead to my second question. The aim of such constraint is because I’m fitting a mixture model of bivariate Gaussians and I want to force one of such components to be responsible of (at least) 5% of the data points. This may seem strange, but it is my intention to separate the tail of the green component -shown in the Figure- into two (green and yellow) during the fitting process instead of performing it as a post-processing step. The red data points belong to a third component. In the figure, the ellipses correspond to the geometrical representation of the Gaussian distributions with a 95% confidence.
That is why I wanted to impose a constraint on the mixing proportions to force the yellow component to be on top of some datapoints -5% at least-. The thing is that the resulting mixing proportion for the yellow component is close to the lower bound (0.05), but it can be seen that the distribution is not on top of any data point (left image). The desired output would be somethin similar to the right image.
Does it make sense to impose a constraint over the mixing proportions in a mixture model in this way?