带显式指数的解映射的上Hölder性质及其在球约束最小二乘问题中的应用
Upper Hölderian with Explicit Exponent of Solution Mapping with Applications to Ball Constrained Least Squares Problems
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中文总结 AI 辅助
本文将Robinson广义方程隐函数定理扩展至上Hölder情形，确定了指数依赖关系，并证明球约束线性最小二乘解映射局部指数为1/3的上Hölder连续性，进而推广至参数情形，为相关问题提供了理论支撑。
中文摘要 AI 辅助
本文将著名的Robinson广义方程隐函数定理从上Lipschitz情形扩展到上Hölder情形，确定了广义方程与其线性化之间显式指数的依赖关系，研究了其在球约束最小二乘问题（包括线性最小二乘和可分非线性最小二乘）中的应用。特别地，我们证明了线性扰动下球约束线性最小二乘的解映射局部具有指数为1/3的上Hölder连续性，这本身具有重要意义。利用上Hölder型隐函数定理，我们证明了参数球约束线性最小二乘的解映射局部具有上Hölder性质。
英文摘要
In this paper, we propose an extension of the well-known Robinson implicit function theorem for generalized equations from the upper Lipschitzian case to the upper Hölderian case. Explicit exponents dependence between the generalized equation and its linearization is determined. Applications to ball constrained least squares problems, including linear least squares and separable nonlinear least squares, are studied. In particular, we establish that the solution mapping of ball constrained linear least squares under linear perturbation is locally upper Hölder continuous with exponent $1/3$, which is of independent interest. Ultilizing the upper Hölderian version of the implicit function theorem, we show the local upper Hölderian of the solution mapping of parametric ball constrained linear least squares.
