Abstract
In this paper, we present a symbolic computation method for constructing a small neighborhood U around a known local optimal maximal or minimal point \(x_0\) of a given smooth function \(f: {\mathbb {R}}^n\rightarrow {\mathbb {R}}\) that contains radical or rational expressions of several variables, so that \(x_0\) is also the global optimal point of f(x) restricted to the small neighborhood U. The constructed small neighborhood can be used to prove that \(f(x_0)\) is the global optimum of f in a rather large region M with \(U\subset M\) via exact numeric computation like interval evaluation and branch-and-bound technology.
Supported by National Natural Science Foundation of China (12171159, 12071282).
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We are grateful to the anonymous reviewers of the ISSAC 2022 and the CASC 2022 for their insightful comments and helpful suggestions, both on mathematics and language aspects, to our manuscripts.
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Zeng, Z., Xu, Y., Chen, Y., Yang, Z. (2022). A Mechanical Method for Isolating Locally Optimal Points of Certain Radical Functions. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2022. Lecture Notes in Computer Science, vol 13366. Springer, Cham. https://doi.org/10.1007/978-3-031-14788-3_21
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