Independent vector analysis (IVA) generalizes independent component analysis (ICA) to multiple datasets, and when used with a multivariate Gaussian model (IVA-G), provides a powerful tool for joint analysis of multiple datasets in an array of applications. While IVA-G enjoys uniqueness guarantees, the current solution to the problem exhibits significant variability across runs necessitating the use of a scheme for selecting the most consistent one, which is costly. In this paper, we present a penalized maximum-likelihood framework for the problem, which enables us to derive a non-convex cost function that depends on the precision matrices of the source component vectors, the main mechanism by which IVA-G leverages correlation across the datasets. By adding a quadratic regularization, a block-coordinate proximal algorithm is shown to offer a suitable solution to this minimization problem. The proposed method also provides convergence guarantees that are lacking in other state-ofthe-art approaches to the problem. This also allows us to obtain overall slightly better performance, and in particular, we show that our method yields better estimation in average than the current IVA-G algorithm for various source numbers, datasets, and degrees of correlation across the data.