  Context. Determining stellar characteristics such as the radius, the mass or
the age is crucial when studying stellar evolution, exoplanetary systems or
characterising stellar populations in the Galaxy. Asteroseismology is the
golden path to accurately obtain these characteristics. In this context, a key
question is how to make these methods less model-dependant. Aims. Building on
the work of Reese et al. (2012), we wish to extend the SOLA inversion technique
to new stellar global characteristics in addition to the mean density. The goal
is to provide a general framework in which to estimate these characteristics as
accurately as possible in low mass main sequence stars. Methods. First, we
describe our framework and discuss the reliability of the inversion technique
and the possible sources of error.We then apply this methodology to the
acoustic radius, an age indicator based on the sound speed derivative and the
mean density and compare it to estimates based on the average large and small
frequency separations. These inversions are carried out for several test cases
which include: various metallicities, different mixing-lengths, non-adiabatic
effects and turbulent pressure. Results. We observe that the SOLA method yields
accurate results in all test cases whereas results based on the large and small
frequency separations are less accurate and more sensitive to surface effects
and structural differences in the models. If we include the surface corrections
of Kjeldsen et al. (2008), we obtain results of comparable accuracy for the
mean density. Overall, the mean density and acoustic radius inversions are more
robust than the inversions for the age indicator. Moreover, the current
approach is limited to relatively young stars with radiative cores. Increasing
the number of observed frequencies improves the reliability and accuracy of the
method.
