mu_min:

Minimum value for barrier parameter. $\;$
This option specifies the lower bound on the barrier parameter in the adaptive mu selection mode. By default, it is set to the minimum of 1e-11 and min("tol","compl_inf_tol")/("barrier_tol_fact- or"+1), which should be a reasonable value. (Only used if option "mu_strategy" is chosen as "adaptive".) The valid range for this real option is $0 < {\tt mu\_min } < {\tt +inf}$ and its default value is $1 \cdot 10^{-11}$.