Trust region methods

Trust region methods are optimization techniques used to find the best solution by iteratively improving a model of a complicated function. At each step, they create a local approximation—called a model—around the current point. The method then searches for a better point within a "trust region," a small area where the model is considered reliable. If the step improves the objective, the region may expand; if not, it shrinks. This approach balances exploration and caution, ensuring steady progress toward the optimal solution while managing uncertainty in the model's accuracy.