A Mechanical Method for Isolating Locally Optimal Points of Certain Radical Functions

Zhenbing Zeng; Yaochen Xu; Yu Chen; Zhengfeng Yang

doi:10.1007/978-3-031-14788-3_21

A Mechanical Method for Isolating Locally Optimal Points of Certain Radical Functions

Zhenbing Zeng, Yaochen Xu, Yu Chen, Zhengfeng Yang

Software Engineering Institute

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

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 x₀ of a given smooth function f: Rⁿ→ R that contains radical or rational expressions of several variables, so that x₀ 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(x₀) is the global optimum of f in a rather large region M with U⊂ M via exact numeric computation like interval evaluation and branch-and-bound technology.

Original language	English
Title of host publication	Computer Algebra in Scientific Computing - 24th International Workshop, CASC 2022, Proceedings
Editors	François Boulier, Matthew England, Timur M. Sadykov, Evgenii V. Vorozhtsov
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	377-396
Number of pages	20
ISBN (Print)	9783031147876
DOIs	https://doi.org/10.1007/978-3-031-14788-3_21
State	Published - 2022
Event	24th International Workshop on Computer Algebra in Scientific Computing, CASC 2022 - Gebze, Turkey Duration: 22 Aug 2022 → 26 Aug 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13366 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	24th International Workshop on Computer Algebra in Scientific Computing, CASC 2022
Country/Territory	Turkey
City	Gebze
Period	22/08/22 → 26/08/22

Keywords

Isolating algorithm
Locally optimal points
Radical function
Symbolic computation

Access to Document

10.1007/978-3-031-14788-3_21

Cite this

Zeng, Z., Xu, Y., Chen, Y., & Yang, Z. (2022). A Mechanical Method for Isolating Locally Optimal Points of Certain Radical Functions. In F. Boulier, M. England, T. M. Sadykov, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing - 24th International Workshop, CASC 2022, Proceedings (pp. 377-396). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13366 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-14788-3_21

Zeng, Zhenbing ; Xu, Yaochen ; Chen, Yu et al. / A Mechanical Method for Isolating Locally Optimal Points of Certain Radical Functions. Computer Algebra in Scientific Computing - 24th International Workshop, CASC 2022, Proceedings. editor / François Boulier ; Matthew England ; Timur M. Sadykov ; Evgenii V. Vorozhtsov. Springer Science and Business Media Deutschland GmbH, 2022. pp. 377-396 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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 x0 of a given smooth function f: Rn→ R that contains radical or rational expressions of several variables, so that x0 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(x0) is the global optimum of f in a rather large region M with U⊂ M via exact numeric computation like interval evaluation and branch-and-bound technology.",

keywords = "Isolating algorithm, Locally optimal points, Radical function, Symbolic computation",

author = "Zhenbing Zeng and Yaochen Xu and Yu Chen and Zhengfeng Yang",

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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 F Boulier, M England, TM Sadykov & EV Vorozhtsov (eds), Computer Algebra in Scientific Computing - 24th International Workshop, CASC 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13366 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 377-396, 24th International Workshop on Computer Algebra in Scientific Computing, CASC 2022, Gebze, Turkey, 22/08/22. https://doi.org/10.1007/978-3-031-14788-3_21

A Mechanical Method for Isolating Locally Optimal Points of Certain Radical Functions. / Zeng, Zhenbing; Xu, Yaochen; Chen, Yu et al.
Computer Algebra in Scientific Computing - 24th International Workshop, CASC 2022, Proceedings. ed. / François Boulier; Matthew England; Timur M. Sadykov; Evgenii V. Vorozhtsov. Springer Science and Business Media Deutschland GmbH, 2022. p. 377-396 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13366 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Zeng Z, Xu Y, Chen Y, Yang Z. A Mechanical Method for Isolating Locally Optimal Points of Certain Radical Functions. In Boulier F, England M, Sadykov TM, Vorozhtsov EV, editors, Computer Algebra in Scientific Computing - 24th International Workshop, CASC 2022, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 377-396. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-14788-3_21