Fraction of Cauchy decrease
= Fraction of Cauchy decrease
{c}
A feasible trial step $s_k$ achieves a fixed <Fraction of Cauchy decrease> if $m_k(0)-m_k(s_k)\geq\kappa[m_k(0)-m_k(s_{C,k})]$ for one constant $\kappa\in(0,1]$ independent of $k$. The <Cauchy decrease bound> then supplies a quantitative model decrease without solving the <trust-region subproblem> exactly. Both the fraction and the relevant model regularity must be controlled in a convergence argument.