Trust-region subproblem
= Trust-region subproblem
{title2=$\min_{\|s\|\leq\Delta}\{a+g^Ts+\tfrac12s^THs\}$}
The <trust-region subproblem> minimizes a <quadratic function> on a closed <Euclidean ball>. Even if $H$ has a negative <eigenvalue>, the <compactness> of this ball guarantees a <global minimum>. An exact answer is often unnecessary: a fixed fraction of the <Cauchy decrease bound> supplies a useful inexpensive standard.