Computable analysis of linear rearrangement optimization

Amin Farjudian

doi:10.1007/978-3-030-14812-6_11

Computable analysis of linear rearrangement optimization

Amin Farjudian^*

^*Corresponding author for this work

Mathematics

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

Abstract

Optimization problems over rearrangement classes arise in various areas such as mathematics, fluid mechanics, biology, and finance. When the generator of the rearrangement class is two-valued, they reduce to shape optimization and free boundary problems which can exhibit intriguing symmetry breaking phenomena. A robust framework is required for computable analysis of these problems. In this paper, as a first step towards such a robust framework, we provide oracle Turing machines that compute the distribution function, decreasing rearrangement, and linear rearrangement optimizers, with respect to functions that are continuous and have no significant flat zones. This assumption on the reference function is necessary, as otherwise, the aforementioned operations may not be computable. We prove that the results can be computed to within any degree of accuracy, conforming to the framework of Type-II Theory of Effectivity.

Original language	English
Title of host publication	Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings
Editors	T. V. Gopal, Junzo Watada
Publisher	Springer Verlag
Pages	172-187
Number of pages	16
ISBN (Print)	9783030148119
DOIs	https://doi.org/10.1007/978-3-030-14812-6_11
Publication status	Published - 2019
Event	15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019 - Kitakyushu, Japan Duration: 13 Apr 2019 → 16 Apr 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11436 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019
Country/Territory	Japan
City	Kitakyushu
Period	13/04/19 → 16/04/19

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2019.

Keywords

Computable analysis
Optimization
Rearrangements of functions

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-14812-6_11

Cite this

Farjudian, A. (2019). Computable analysis of linear rearrangement optimization. In T. V. Gopal, & J. Watada (Eds.), Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings (pp. 172-187). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11436 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-14812-6_11

Farjudian, Amin. / Computable analysis of linear rearrangement optimization. Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings. editor / T. V. Gopal ; Junzo Watada. Springer Verlag, 2019. pp. 172-187 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Optimization problems over rearrangement classes arise in various areas such as mathematics, fluid mechanics, biology, and finance. When the generator of the rearrangement class is two-valued, they reduce to shape optimization and free boundary problems which can exhibit intriguing symmetry breaking phenomena. A robust framework is required for computable analysis of these problems. In this paper, as a first step towards such a robust framework, we provide oracle Turing machines that compute the distribution function, decreasing rearrangement, and linear rearrangement optimizers, with respect to functions that are continuous and have no significant flat zones. This assumption on the reference function is necessary, as otherwise, the aforementioned operations may not be computable. We prove that the results can be computed to within any degree of accuracy, conforming to the framework of Type-II Theory of Effectivity.",

keywords = "Computable analysis, Optimization, Rearrangements of functions",

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note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2019.; 15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019 ; Conference date: 13-04-2019 Through 16-04-2019",

year = "2019",

doi = "10.1007/978-3-030-14812-6_11",

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Farjudian, A 2019, Computable analysis of linear rearrangement optimization. in TV Gopal & J Watada (eds), Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11436 LNCS, Springer Verlag, pp. 172-187, 15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019, Kitakyushu, Japan, 13/04/19. https://doi.org/10.1007/978-3-030-14812-6_11

Computable analysis of linear rearrangement optimization. / Farjudian, Amin.
Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings. ed. / T. V. Gopal; Junzo Watada. Springer Verlag, 2019. p. 172-187 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11436 LNCS).

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

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N2 - Optimization problems over rearrangement classes arise in various areas such as mathematics, fluid mechanics, biology, and finance. When the generator of the rearrangement class is two-valued, they reduce to shape optimization and free boundary problems which can exhibit intriguing symmetry breaking phenomena. A robust framework is required for computable analysis of these problems. In this paper, as a first step towards such a robust framework, we provide oracle Turing machines that compute the distribution function, decreasing rearrangement, and linear rearrangement optimizers, with respect to functions that are continuous and have no significant flat zones. This assumption on the reference function is necessary, as otherwise, the aforementioned operations may not be computable. We prove that the results can be computed to within any degree of accuracy, conforming to the framework of Type-II Theory of Effectivity.

AB - Optimization problems over rearrangement classes arise in various areas such as mathematics, fluid mechanics, biology, and finance. When the generator of the rearrangement class is two-valued, they reduce to shape optimization and free boundary problems which can exhibit intriguing symmetry breaking phenomena. A robust framework is required for computable analysis of these problems. In this paper, as a first step towards such a robust framework, we provide oracle Turing machines that compute the distribution function, decreasing rearrangement, and linear rearrangement optimizers, with respect to functions that are continuous and have no significant flat zones. This assumption on the reference function is necessary, as otherwise, the aforementioned operations may not be computable. We prove that the results can be computed to within any degree of accuracy, conforming to the framework of Type-II Theory of Effectivity.

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Farjudian A. Computable analysis of linear rearrangement optimization. In Gopal TV, Watada J, editors, Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings. Springer Verlag. 2019. p. 172-187. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-14812-6_11

Computable analysis of linear rearrangement optimization

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this