Overview of Trust-region Methods

The trust-region technique is an optimization algorithm for solving multidimensional nonlinear optimization complications. It is a class of derivative-based optimization approaches that relies on information about the gradient of the objective function and possibly Hessians. The main idea behind the Trust-region method is to remodel the objective function around the present iteration Solution of the inner subproblem. The confidence region is the region around the present iteration where the model is expected to be accurate. At each iteration, the trust region technique uses a quadratic model to estimate the objective function locally (Yuan, 2019). This model is based on the current iteration and the information about the gradient and Hessian. The confidence region limits the distance the algorithm can take from the current iteration to find the next one. The size of the trust region is adjusted dynamically based on the arrangement between the model and the actual performance values.