The Jacobian Consistency of a One-Parametric Class of Smoothing Functions for SOCCP
Second-order cone (SOC) complementarity functions and their smoothing functions have been much studied in the solution of second-order cone complementarity problems (SOCCP). In this paper, we study the directional derivative and B-subdifferential of the one-parametric class of SOC complementarity fu...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/965931 |
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| author | Xiaoni Chi Zhongping Wan Zijun Hao |
| author_facet | Xiaoni Chi Zhongping Wan Zijun Hao |
| author_sort | Xiaoni Chi |
| collection | DOAJ |
| description | Second-order cone (SOC) complementarity functions and their smoothing functions have been much studied in the solution of second-order cone complementarity problems (SOCCP). In this paper, we study the directional derivative and B-subdifferential of the one-parametric class of SOC complementarity functions, propose its smoothing function, and derive the computable formula for the Jacobian of the smoothing function. Based on these results, we prove the Jacobian consistency of the one-parametric class of smoothing functions, which will play an important role for achieving the rapid convergence of smoothing methods. Moreover, we estimate the distance between the subgradient of the one-parametric class of the SOC complementarity functions and the gradient of its smoothing function, which will help to adjust a parameter appropriately in smoothing methods. |
| format | Article |
| id | doaj-art-d6b268746ace4800907f3a08c190965f |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d6b268746ace4800907f3a08c190965f2025-08-20T03:23:39ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/965931965931The Jacobian Consistency of a One-Parametric Class of Smoothing Functions for SOCCPXiaoni Chi0Zhongping Wan1Zijun Hao2School of Mathematics and Statistics, Wuhan University, Wuhan 430072, ChinaSchool of Mathematics and Statistics, Wuhan University, Wuhan 430072, ChinaSchool of Mathematics and Statistics, Wuhan University, Wuhan 430072, ChinaSecond-order cone (SOC) complementarity functions and their smoothing functions have been much studied in the solution of second-order cone complementarity problems (SOCCP). In this paper, we study the directional derivative and B-subdifferential of the one-parametric class of SOC complementarity functions, propose its smoothing function, and derive the computable formula for the Jacobian of the smoothing function. Based on these results, we prove the Jacobian consistency of the one-parametric class of smoothing functions, which will play an important role for achieving the rapid convergence of smoothing methods. Moreover, we estimate the distance between the subgradient of the one-parametric class of the SOC complementarity functions and the gradient of its smoothing function, which will help to adjust a parameter appropriately in smoothing methods.http://dx.doi.org/10.1155/2013/965931 |
| spellingShingle | Xiaoni Chi Zhongping Wan Zijun Hao The Jacobian Consistency of a One-Parametric Class of Smoothing Functions for SOCCP Abstract and Applied Analysis |
| title | The Jacobian Consistency of a One-Parametric Class of Smoothing Functions for SOCCP |
| title_full | The Jacobian Consistency of a One-Parametric Class of Smoothing Functions for SOCCP |
| title_fullStr | The Jacobian Consistency of a One-Parametric Class of Smoothing Functions for SOCCP |
| title_full_unstemmed | The Jacobian Consistency of a One-Parametric Class of Smoothing Functions for SOCCP |
| title_short | The Jacobian Consistency of a One-Parametric Class of Smoothing Functions for SOCCP |
| title_sort | jacobian consistency of a one parametric class of smoothing functions for soccp |
| url | http://dx.doi.org/10.1155/2013/965931 |
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