#### Cubic overestimation and secant updating for unconstrained optimization of C2,1 functions

The discrepancy between an objective function f and its local quadratic model f(x)+∇ f(x)⊤ s+s⊤ H(x) s/2 ≈ f(x+s) at the current iterate x is estimated using a cubic term q |s|3/3. Potential steps are chosen such that they minimize (or at least significantly reduce) the overestimating function ∇ f(x)⊤ s+s⊤ B s/2+q |s|3/3 with B ≈ H(x). This ensures f(x+s)