一致q阶增长条件
The Uniform q-Order Growth Condition
摘要: 一致二阶增长条件是优化中的重要概念，已被广泛研究。近来，作为一致二阶增长条件的自然推广，用一般的正数q代替二，文献[1]引进并研究了一致q阶增长条件。本文在文献[1]的基础上，进一步考虑q-正则函数f的一致q阶增长条件，通过q-正则函数f之次微分映射∂f的Hölder度量正则性刻画了f的一致q阶增长条件。特别地，本文给出了∂f的Hölder度量正则性所涉及模及半径与f的一致q阶增长条件涉及半径之间的确切数量关系，从而改进了一致二阶增长条件及一致q阶增长条件方面的一些现有结果。
Abstract: Uniform second order growth condition is an important notion in optimization and has been studied extensively. Recently, as a natural extension of the uniform second order growth condition, with a positive number q replacing 2, the uniform q-order growth condition was introduced and studied in [1]. Motivated by [1], this thesis further studies the uniform q-order growth condition of a q-order regular real-valued function f. In terms of the Hölder metric regularity of the subdifferential mapping ∂f, we provide sufficient and necessary conditions for f to have the uniform q-order growth condition. In particular, using the modulus and radius appearing in the Hölder metric regularity of the subdifferential mapping ∂f, we give an exact quantitative formula of the radius appearing in the uniform q-order growth condition, which improves some existing results on the uniform second order growth condition and uniform q-order growth condition.
文章引用：杨吉根, 吕鹏辉, 陈斌. 一致q阶增长条件[J]. 应用数学进展, 2019, 8(1): 119-134. https://doi.org/10.12677/AAM.2019.81014

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