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• W2754296883 abstract "In this paper, we consider the convergence of an abstract inexact nonconvex and nonsmooth algorithm. We promise a pseudo sufficient descent condition and a pseudo relative error condition, which are both related to an auxiliary sequence, for the algorithm; and a continuity condition is assumed to hold. In fact, a lot of classical inexact nonconvex and nonsmooth algorithms allow these three conditions. Under a special kind of summable assumption on the auxiliary sequence, we prove the sequence generated by the general algorithm converges to a critical point of the objective function if being assumed Kurdyka- Lojasiewicz property. The core of the proofs lies in building a new Lyapunov function, whose successive difference provides a bound for the successive difference of the points generated by the algorithm. And then, we apply our findings to several classical nonconvex iterative algorithms and derive the corresponding convergence results" @default.
• W2754296883 created "2017-09-25" @default.
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• W2754296883 date "2017-09-12" @default.
• W2754296883 modified "2023-09-25" @default.
• W2754296883 title "A convergence framework for inexact nonconvex and nonsmooth algorithms and its applications to several iterations" @default.
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• W2754296883 doi "https://doi.org/10.48550/arxiv.1709.04072" @default.
• W2754296883 hasPublicationYear "2017" @default.
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