Multivariate Lipschitz optimization: Survey and computational comparison
Abstract
Many methods have been proposed to minimize a multivariate Lipschitz function on a box. They pertain the three approaches: (i) reduction to the univariate case by projection (Pijavskii) or by using a space-filling curve (Strongin); (ii) construction and refinement of a single upper bounding function (Pijavskii, Mladineo, Mayne and Polak, Jaumard Hermann and Ribault, Wood...); (iii) branch and bound with local upper bounding functions (Galperin, Pint{acute e}r, Meewella and Mayne, the present authors). A survey is made, stressing similarities of algorithms, expressed when possible within a unified framework. Moreover, an extensive computational comparison is reported on.
- Authors:
- Publication Date:
- OSTI Identifier:
- 36111
- Report Number(s):
- CONF-9408161-
TRN: 94:009753-0385
- Resource Type:
- Conference
- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; MATRICES; NUMERICAL SOLUTION; EFFICIENCY; ALGORITHMS; VARIATIONAL METHODS
Citation Formats
Hansen, P, Gourdin, E, and Jaumard, B. Multivariate Lipschitz optimization: Survey and computational comparison. United States: N. p., 1994.
Web.
Hansen, P, Gourdin, E, & Jaumard, B. Multivariate Lipschitz optimization: Survey and computational comparison. United States.
Hansen, P, Gourdin, E, and Jaumard, B. 1994.
"Multivariate Lipschitz optimization: Survey and computational comparison". United States.
@article{osti_36111,
title = {Multivariate Lipschitz optimization: Survey and computational comparison},
author = {Hansen, P and Gourdin, E and Jaumard, B},
abstractNote = {Many methods have been proposed to minimize a multivariate Lipschitz function on a box. They pertain the three approaches: (i) reduction to the univariate case by projection (Pijavskii) or by using a space-filling curve (Strongin); (ii) construction and refinement of a single upper bounding function (Pijavskii, Mladineo, Mayne and Polak, Jaumard Hermann and Ribault, Wood...); (iii) branch and bound with local upper bounding functions (Galperin, Pint{acute e}r, Meewella and Mayne, the present authors). A survey is made, stressing similarities of algorithms, expressed when possible within a unified framework. Moreover, an extensive computational comparison is reported on.},
doi = {},
url = {https://www.osti.gov/biblio/36111},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sat Dec 31 00:00:00 EST 1994},
month = {Sat Dec 31 00:00:00 EST 1994}
}
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