Model-Based Descent

Model-based methods in DFO proceed from the idea that if it is possible to build a “good” model of the true objective function, then information from the model can be used to guide the optimization. In Chapter 9 , we studied several methods for constructing model functions using only objective function evaluations. We also defined fully linear, as a term to mean that the optimiser has access to an accuracy parameter $$\Delta $$ that can be used to drive the error in the model to 0 in a predictable way. We now turn our attention to how to employ model functions in unconstrained DFO algorithms.