TY - GEN
T1 - Computable analysis of linear rearrangement optimization
AU - Farjudian, Amin
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019
Y1 - 2019
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.
KW - Computable analysis
KW - Optimization
KW - Rearrangements of functions
UR - http://www.scopus.com/inward/record.url?scp=85064867271&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-14812-6_11
DO - 10.1007/978-3-030-14812-6_11
M3 - Conference contribution
AN - SCOPUS:85064867271
SN - 9783030148119
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 172
EP - 187
BT - Theory and Applications of Models of Computation - 15th Annual Conference, TAMC 2019, Proceedings
A2 - Gopal, T. V.
A2 - Watada, Junzo
PB - Springer Verlag
T2 - 15th Annual Conference on Theory and Applications of Models of Computation, TAMC 2019
Y2 - 13 April 2019 through 16 April 2019
ER -