  This note concerns a class of nonmonotone descent methods for minimizing a
proper lower semicontinuous Kurdyka-{\L}$\ddot{o}$jasiewicz (KL) function
$\Phi$, whose iterate sequence obeys the ZH-type nonmonotone decrease condition
and a relative error condition. We prove that the iterate sequence converges to
a critical point of $\Phi$, and if $\Phi$ has the KL property of exponent
$\theta\in(0,1)$ at this critical point, the convergence has a linear rate for
$\theta\in(0,1/2]$ and a sublinear rate of exponent
$\frac{1-\theta}{1-2\theta}$ for $\theta\in(1/2,1)$. Our results first resolve
the full convergence of the iterate sequence generated by the ZH-type
nonmonotone descent method for nonconvex and nonsmooth optimization problems,
and extend the full convergence of monotone descent methods for KL optimization
problems to the ZH-type nonmonotone descent method.
