On the equivalence between the modifier-adaptation and trust-region frameworks

In this short note, the recently popular modifier-adaptation framework for real-time optimization is discussed in tandem with the well-developed trustregion framework of numerical optimization, and it is shown that the basic version of the former is simply a special case of the latter. This relation is then exploited to propose a globally convergent modifier-adaptation algorithm using already developed trust-region theory. Cases when the two are not equivalent are also discussed.