This study presents a novel quadratic programming based approach to glottal inverse filtering. The proposed method aims to jointly model the effect of the vocal tract and lip radiation with a single filter whose coefficients are optimized using the quadratic programming framework. This allows the proposed method to directly estimate the glottal flow of speech, which mitigates the problem of non-flat closed phases in inverse filtering estimates. The proposed method was objectively evaluated using a synthetic Liljencrants-Fant model based test set of sustained vowels containing a wide variety of phonation types and fundamental periods. The results indicate that the proposed method is robust to changes in f0 and state-of-the-art quality results were obtained for high pitch voices, when f0 is in the range 330 to 450Hz.