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 trust-region framework of numerical optimization, and it is shown that the basic version of the former is a simplification of the latter when the problem is unconstrained. This relation is then exploited to propose a globally convergent modifier-adaptation algorithm using already developed trust-region theory. Cases when the two may not be equivalent and extensions to constrained problems are also discussed.