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Article: A Point Balance Algorithm for the Spherical Code Problem
Title | A Point Balance Algorithm for the Spherical Code Problem |
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Authors | |
Keywords | Bilevel optimization Global optimization Pattern search algorithm Spherical code (SC) Extremal spherical code Balanced spherical code Extremal energy Point balance algorithm |
Issue Date | 2001 |
Citation | Journal of Global Optimization, 2001, v. 19, n. 4, p. 329-344 How to Cite? |
Abstract | The Spherical Code (SC) problem has many important applications in such fields as physics, molecular biology, signal transmission, chemistry, engineering and mathematics. This paper presents a bilevel optimization formulation of the SC problem. Based on this formulation, the concept of balanced spherical code is introduced and a new approach, the Point Balance Algorithm (PBA), is presented to search for a 1-balanced spherical code. Since an optimal solution of the SC problem (an extremal spherical code) must be a 1-balanced spherical code, PBA can be applied easily to search for an extremal spherical code. In addition, given a certain criterion, PBA can generate efficiently an approximate optimal spherical code on a sphere in the n-dimensional space ℛn. Some implementation issues of PBA are discussed and putative global optimal solutions of the Fekete problem in 3, 4 and 5-dimensional space are also reported. Finally, an open question about the geometry of Fekete points on the unit sphere in the 3-dimensional space is posed. |
Persistent Identifier | http://hdl.handle.net/10722/296016 |
ISSN | 2023 Impact Factor: 1.3 2023 SCImago Journal Rankings: 0.743 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Huang, Hong Xuan | - |
dc.contributor.author | Pardalos, Panos M. | - |
dc.contributor.author | Shen, Zuo Jun | - |
dc.date.accessioned | 2021-02-11T04:52:39Z | - |
dc.date.available | 2021-02-11T04:52:39Z | - |
dc.date.issued | 2001 | - |
dc.identifier.citation | Journal of Global Optimization, 2001, v. 19, n. 4, p. 329-344 | - |
dc.identifier.issn | 0925-5001 | - |
dc.identifier.uri | http://hdl.handle.net/10722/296016 | - |
dc.description.abstract | The Spherical Code (SC) problem has many important applications in such fields as physics, molecular biology, signal transmission, chemistry, engineering and mathematics. This paper presents a bilevel optimization formulation of the SC problem. Based on this formulation, the concept of balanced spherical code is introduced and a new approach, the Point Balance Algorithm (PBA), is presented to search for a 1-balanced spherical code. Since an optimal solution of the SC problem (an extremal spherical code) must be a 1-balanced spherical code, PBA can be applied easily to search for an extremal spherical code. In addition, given a certain criterion, PBA can generate efficiently an approximate optimal spherical code on a sphere in the n-dimensional space ℛn. Some implementation issues of PBA are discussed and putative global optimal solutions of the Fekete problem in 3, 4 and 5-dimensional space are also reported. Finally, an open question about the geometry of Fekete points on the unit sphere in the 3-dimensional space is posed. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of Global Optimization | - |
dc.subject | Bilevel optimization | - |
dc.subject | Global optimization | - |
dc.subject | Pattern search algorithm | - |
dc.subject | Spherical code (SC) | - |
dc.subject | Extremal spherical code | - |
dc.subject | Balanced spherical code | - |
dc.subject | Extremal energy | - |
dc.subject | Point balance algorithm | - |
dc.title | A Point Balance Algorithm for the Spherical Code Problem | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1023/A:1011246928813 | - |
dc.identifier.scopus | eid_2-s2.0-0035304568 | - |
dc.identifier.volume | 19 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 329 | - |
dc.identifier.epage | 344 | - |
dc.identifier.isi | WOS:000167852500001 | - |
dc.identifier.issnl | 0925-5001 | - |