Calculus Rules of the Generalized Concave Kurdyka–Łojasiewicz Property

Xianfu Wang () and Ziyuan Wang ()
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Xianfu Wang: University of British Columbia
Ziyuan Wang: University of British Columbia

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 3, No 1, 839-854

Abstract: Abstract In this paper, we propose several calculus rules for the generalized concave Kurdyka–Łojasiewicz (KL) property, which generalize Li and Pong’s results for KL exponents. The optimal concave desingularizing function has various forms and may be nondifferentiable. Our calculus rules do not assume desingularizing functions to have any specific form nor differentiable, while the known results do. Several examples are also given to show that our calculus rules are applicable to a broader class of functions than the known ones.

Keywords: The generalized concave Kurdyka–Łojasiewicz property; Optimal concave desingularizing function; Calculus rules; The Kurdyka–Łojasiewicz property.; Primary 49J53; 26D10; 90C26; Secondary 26A51; 26B25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02219-y

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