In optimization, particularly in the context of nonlinear optimization problems, a **trust region** is a strategy used to improve the convergence of algorithms. It refers to a region around the current point in which the optimization algorithm trusts that a model of the objective function is accurate enough to make reliable decisions.
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A trust region restricts a local approximation to a neighborhood where it is expected to model the objective function accurately. A quadratic model is , where and is a symmetric matrix approximating the Hessian matrix. Minimizing this quadratic function over a Euclidean ball of radius is the trust-region subproblem. The trust-region acceptance ratio then checks the model against the actual objective function.