1. Convergence of ZH-type nonmonotone descent method for Kurdyka-{\L}ojasiewicz optimization problems
- Author
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Qian, Yitian, Tao, Ting, Pan, Shaohua, and Qi, Houduo
- Subjects
Mathematics - Optimization and Control - Abstract
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.
- Published
- 2024