Upper H\"olderian with Explicit Exponent of Solution Mapping with Applications to Ball Constrained Least Squares Problems

Yu Wang; Shenglong Hu

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arXiv · 2608.22436

Upper H\"olderian with Explicit Exponent of Solution Mapping with Applications to Ball Constrained Least Squares Problems

Yu Wang·Shenglong Hu

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Abstract

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 H\"olderian 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 H\"older continuous with exponent $1/3$, which is of independent interest. Ultilizing the upper H\"olderian version of the implicit function theorem, we show the local upper H\"olderian of the solution mapping of parametric ball constrained linear least squares.

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Yu Wang, Shenglong Hu. 2026-08-23. Upper H\"olderian with Explicit Exponent of Solution Mapping with Applications to Ball Constrained Least Squares Problems. https://arxiv.org/abs/2608.22436

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