Kernel-Based Interior-Point Methods for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones
We present an interior point method for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones (SCLCPs). The Cartesian P*(k)-SCLCPs have been recently introduced as the generalization of the more commonly known and more widely used monotone SCLCPs. The IPM is based on the barrier funct...
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| Format: | Article |
| Language: | English |
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Croatian Operational Research Society
2011-02-01
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| Series: | Croatian Operational Research Review |
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| Online Access: | http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=142164 |
| _version_ | 1818446398388961280 |
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| author | Goran Lešaja |
| author_facet | Goran Lešaja |
| author_sort | Goran Lešaja |
| collection | DOAJ |
| description | We present an interior point method for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones (SCLCPs). The Cartesian P*(k)-SCLCPs have been recently introduced as the generalization of the more commonly known and more widely used monotone SCLCPs. The IPM is based on the barrier functions that are defined by a large class of univariate functions called eligible kernel function which have recently been successfully used to design new IPMs for various optimization problems. Eligible barrier (kernel) functions are used in calculating the Nesterov-Todd search directions and the default step-size which leads to a very good complexity results for the method. For some specific eligilbe kernel functions we match the best known iteration bound for the long-step methods while for the short-step methods the best iteration bound is matched for all cases. |
| first_indexed | 2024-12-14T19:47:05Z |
| format | Article |
| id | doaj.art-27904533787344278f226e6e709a840f |
| institution | Directory Open Access Journal |
| issn | 1848-0225 1848-9931 |
| language | English |
| last_indexed | 2024-12-14T19:47:05Z |
| publishDate | 2011-02-01 |
| publisher | Croatian Operational Research Society |
| record_format | Article |
| series | Croatian Operational Research Review |
| spelling | doaj.art-27904533787344278f226e6e709a840f2022-12-21T22:49:32ZengCroatian Operational Research SocietyCroatian Operational Research Review1848-02251848-99312011-02-01212332Kernel-Based Interior-Point Methods for Cartesian P*(k)-Linear Complementarity Problems over Symmetric ConesGoran Lešaja0Department of Mathematical Sciences, Georgia Suthern University, Statesboro, GA, United States of AmericaWe present an interior point method for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones (SCLCPs). The Cartesian P*(k)-SCLCPs have been recently introduced as the generalization of the more commonly known and more widely used monotone SCLCPs. The IPM is based on the barrier functions that are defined by a large class of univariate functions called eligible kernel function which have recently been successfully used to design new IPMs for various optimization problems. Eligible barrier (kernel) functions are used in calculating the Nesterov-Todd search directions and the default step-size which leads to a very good complexity results for the method. For some specific eligilbe kernel functions we match the best known iteration bound for the long-step methods while for the short-step methods the best iteration bound is matched for all cases.http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=142164linear complementarity problemCartesian P*(k) propertyEuclidean Jordan algebras and symmetric conesinterior-point methodkernel functionspolynomial complexity |
| spellingShingle | Goran Lešaja Kernel-Based Interior-Point Methods for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones Croatian Operational Research Review linear complementarity problem Cartesian P*(k) property Euclidean Jordan algebras and symmetric cones interior-point method kernel functions polynomial complexity |
| title | Kernel-Based Interior-Point Methods for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones |
| title_full | Kernel-Based Interior-Point Methods for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones |
| title_fullStr | Kernel-Based Interior-Point Methods for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones |
| title_full_unstemmed | Kernel-Based Interior-Point Methods for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones |
| title_short | Kernel-Based Interior-Point Methods for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones |
| title_sort | kernel based interior point methods for cartesian p k linear complementarity problems over symmetric cones |
| topic | linear complementarity problem Cartesian P*(k) property Euclidean Jordan algebras and symmetric cones interior-point method kernel functions polynomial complexity |
| url | http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=142164 |
| work_keys_str_mv | AT goranlesaja kernelbasedinteriorpointmethodsforcartesianpklinearcomplementarityproblemsoversymmetriccones |