= Trust region
{title2=$\|s\|\leq\Delta$}
{wiki}
A <trust region> restricts a local approximation to a neighborhood where it is expected to model the <objective function> accurately. A quadratic model is $m(s)=f(x)+g^Ts+\tfrac12s^THs$, where $g=\nabla f(x)$ and $H$ is a <symmetric matrix> approximating the <Hessian matrix>. Minimizing this <quadratic function> over a <Euclidean ball> of radius $\Delta>0$ is the <trust-region subproblem>. The <trust-region acceptance ratio> then checks the model against the actual <objective function>.
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