This paper puts forward a comprehensive study of the design of global stopping criteria for multi-objective optimization. In this study we propose a global stopping criterion, which is terms as MGBM after the authors surnames. MGBM combines a novel progress indicator, called mutual domination rate (MDR) indicator, with a simplified Kalman filter, which is used for evidence-gathering purposes. The MDR indicator, which is also introduced, is a special-purpose progress indicator designed for the purpose of stopping a multi-objective optimization. As part of the paper we describe the criterion from a theoretical perspective and examine its performance on a number of test problems. We also compare this method with similar approaches to the issue. The results of these experiments suggest that MGBM is a valid and accurate approach.