This paper focuses on a class of zero-norm composite optimization problems. For this class of nonconvex nonsmooth problems, we establish the Kurdyka–Łojasiewicz property of exponent being a half for its objective function under a suitable assumption and provide some examples to illustrate that such an assumption is not very restricted which, in particular, involve the zero-norm regularized or constrained piecewise linear–quadratic function, the zero-norm regularized or constrained logistic regression function, the zero-norm regularized or constrained quadratic function over a sphere.

中文翻译：

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零范数复合函数的 Kurdyka–Łojasiewicz 性质

本文重点研究一类零范数复合优化问题。对于这类非凸非光滑问题，我们在合适的假设下为其目标函数建立了指数为一半的 Kurdyka-Łojasiewicz 性质，并提供了一些例子来说明这种假设不是很受限制，特别是涉及零-范数正则化或约束分段线性二次函数，零范数正则化或约束逻辑回归函数，球面上的零范数正则化或约束二次函数。