The path of signals from space geodetic techniques, such as Very Long Baseline Interferometry (VLBI) or Global Navigation Satellite Systems (GNSS), is affected by refractivity variations in the neutral atmosphere. This tropospheric delay, which represents a major contribution to the error budget of space geodetic observations, is generally considered by applying an adequate model (hydrostatic component) and by additionally estimating tropospheric parameters (wet component). Sometimes, the standard approach may lead to negative tropospheric parameters. Due to the fact, that there is nothing like negative water vapour, these negative estimates do not reflect the meteorological conditions in a plausible way.In this paper, we introduce an Inequality Constrained Least Squares (ICLS) method from the field of convex optimization to constrain the tropospheric parameters to non-negative values. We applied this new methodology to 17 years of VLBI sessions. For about 20% of these sessions the method automatically applied inequality constraints. For many sessions the procedure is successful. However, deficiencies in the hydrostatic modeling also lead to worse results for a few sessions. Thus, the methodology is applicable to VLBI data analyses if the a priori modeling is correct which is not always the case for the data set available at the moment.