Computable analysis of linear rearrangement optimization

Research output: Chapter in Book/Conference proceedingConference contributionpeer-review

1 Downloads (Pure)

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 languageEnglish
Title of host publicationTheory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings
EditorsT. V. Gopal, Junzo Watada
PublisherSpringer Verlag
Pages172-187
Number of pages16
ISBN (Print)9783030148119
DOIs
Publication statusPublished - 2019
Event15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019 - Kitakyushu, Japan
Duration: 13 Apr 201916 Apr 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11436 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019
Country/TerritoryJapan
CityKitakyushu
Period13/04/1916/04/19

Keywords

  • Computable analysis
  • Optimization
  • Rearrangements of functions

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

Fingerprint

Dive into the research topics of 'Computable analysis of linear rearrangement optimization'. Together they form a unique fingerprint.

Cite this