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In Sect. 8.1.3 , we introduced the Kurdyka-Łojasiewicz (KL) condition for convex functions. In this chapter, we extend the KL condition to non-convex functions and apply it to analyze algorithms for solving non-smooth optimization problems where the objective functions may lack convexity. Aldditionally, we present numerous examples of functions that satisfy the KL condition. In particular, we demonstrate that semi-algebraic functions belong to the class of KL functions.

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Optimization with Kurdyka-Łojasiewicz Property

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  • 发表日期：

    2025年

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  • Qinian Jin

摘要

In Sect. 8.1.3 , we introduced the Kurdyka-Łojasiewicz (KL) condition for convex functions. In this chapter, we extend the KL condition to non-convex functions and apply it to analyze algorithms for solving non-smooth optimization problems where the objective functions may lack convexity. Aldditionally, we present numerous examples of functions that satisfy the KL condition. In particular, we demonstrate that semi-algebraic functions belong to the class of KL functions.