A new search direction of IPM for horizontal linear complementarity problems
This study presents a new search direction for the horizontal linear complementarity problem. A vector-valued function is applied to the system of xy=μe, which defines the central path. Usually, the way to get the equivalent form of the central path is using the square root function. However, in our...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2023-01-01
|
| Series: | Frontiers in Energy Research |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fenrg.2022.977448/full |
| _version_ | 1797961224187543552 |
|---|---|
| author | Xiaoyu Gong Xiaoyu Gong Lei Xi Lei Xi Bo Yuan |
| author_facet | Xiaoyu Gong Xiaoyu Gong Lei Xi Lei Xi Bo Yuan |
| author_sort | Xiaoyu Gong |
| collection | DOAJ |
| description | This study presents a new search direction for the horizontal linear complementarity problem. A vector-valued function is applied to the system of xy=μe, which defines the central path. Usually, the way to get the equivalent form of the central path is using the square root function. However, in our study, we substitute a new search function formed by a different identity map, which obtains the equivalent shape of the central path using the square root function. We get the new search directions from Newton’s Method. Given this framework, we prove polynomial complexity for the Newton directions. We show that the algorithm’s complexity is O(nlognϵ), which is the same as the best-given algorithms for the horizontal linear complementarity problem. |
| first_indexed | 2024-04-11T00:55:43Z |
| format | Article |
| id | doaj.art-ab0e6f4bea2b4b0791d7caa9b12bca22 |
| institution | Directory Open Access Journal |
| issn | 2296-598X |
| language | English |
| last_indexed | 2024-04-11T00:55:43Z |
| publishDate | 2023-01-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Energy Research |
| spelling | doaj.art-ab0e6f4bea2b4b0791d7caa9b12bca222023-01-05T06:02:28ZengFrontiers Media S.A.Frontiers in Energy Research2296-598X2023-01-011010.3389/fenrg.2022.977448977448A new search direction of IPM for horizontal linear complementarity problemsXiaoyu Gong0Xiaoyu Gong1Lei Xi2Lei Xi3Bo Yuan4School of Economics and Management, China Three Gorges University, Yichang, ChinaYichang Key Laboratory of Information Physics Fusion Defense and Control System (Three Gorges University), Yichang, ChinaYichang Key Laboratory of Information Physics Fusion Defense and Control System (Three Gorges University), Yichang, ChinaCollege of Electrical Engineering and New Energy, China Three Gorges University, Yichang, ChinaCollege of Electrical Engineering and New Energy, China Three Gorges University, Yichang, ChinaThis study presents a new search direction for the horizontal linear complementarity problem. A vector-valued function is applied to the system of xy=μe, which defines the central path. Usually, the way to get the equivalent form of the central path is using the square root function. However, in our study, we substitute a new search function formed by a different identity map, which obtains the equivalent shape of the central path using the square root function. We get the new search directions from Newton’s Method. Given this framework, we prove polynomial complexity for the Newton directions. We show that the algorithm’s complexity is O(nlognϵ), which is the same as the best-given algorithms for the horizontal linear complementarity problem.https://www.frontiersin.org/articles/10.3389/fenrg.2022.977448/fulllinear complementarityinterior-point methodfull-Newton stepcomplexityHLCP |
| spellingShingle | Xiaoyu Gong Xiaoyu Gong Lei Xi Lei Xi Bo Yuan A new search direction of IPM for horizontal linear complementarity problems Frontiers in Energy Research linear complementarity interior-point method full-Newton step complexity HLCP |
| title | A new search direction of IPM for horizontal linear complementarity problems |
| title_full | A new search direction of IPM for horizontal linear complementarity problems |
| title_fullStr | A new search direction of IPM for horizontal linear complementarity problems |
| title_full_unstemmed | A new search direction of IPM for horizontal linear complementarity problems |
| title_short | A new search direction of IPM for horizontal linear complementarity problems |
| title_sort | new search direction of ipm for horizontal linear complementarity problems |
| topic | linear complementarity interior-point method full-Newton step complexity HLCP |
| url | https://www.frontiersin.org/articles/10.3389/fenrg.2022.977448/full |
| work_keys_str_mv | AT xiaoyugong anewsearchdirectionofipmforhorizontallinearcomplementarityproblems AT xiaoyugong anewsearchdirectionofipmforhorizontallinearcomplementarityproblems AT leixi anewsearchdirectionofipmforhorizontallinearcomplementarityproblems AT leixi anewsearchdirectionofipmforhorizontallinearcomplementarityproblems AT boyuan anewsearchdirectionofipmforhorizontallinearcomplementarityproblems AT xiaoyugong newsearchdirectionofipmforhorizontallinearcomplementarityproblems AT xiaoyugong newsearchdirectionofipmforhorizontallinearcomplementarityproblems AT leixi newsearchdirectionofipmforhorizontallinearcomplementarityproblems AT leixi newsearchdirectionofipmforhorizontallinearcomplementarityproblems AT boyuan newsearchdirectionofipmforhorizontallinearcomplementarityproblems |