Nonsmooth Levenberg-Marquardt Type Method for Solving a Class of Stochastic Linear Complementarity Problems with Finitely Many Elements
Our purpose of this paper is to solve a class of stochastic linear complementarity problems (SLCP) with finitely many elements. Based on a new stochastic linear complementarity problem function, a new semi-smooth least squares reformulation of the stochastic linear complementarity problem is introdu...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2016-12-01
|
| Series: | Algorithms |
| Subjects: | |
| Online Access: | http://www.mdpi.com/1999-4893/9/4/83 |
| _version_ | 1818190516297138176 |
|---|---|
| author | Zhimin Liu Shouqiang Du Ruiying Wang |
| author_facet | Zhimin Liu Shouqiang Du Ruiying Wang |
| author_sort | Zhimin Liu |
| collection | DOAJ |
| description | Our purpose of this paper is to solve a class of stochastic linear complementarity problems (SLCP) with finitely many elements. Based on a new stochastic linear complementarity problem function, a new semi-smooth least squares reformulation of the stochastic linear complementarity problem is introduced. For solving the semi-smooth least squares reformulation, we propose a feasible nonsmooth Levenberg–Marquardt-type method. The global convergence properties of the nonsmooth Levenberg–Marquardt-type method are also presented. Finally, the related numerical results illustrate that the proposed method is efficient for the related refinery production problem and the large-scale stochastic linear complementarity problems. |
| first_indexed | 2024-12-11T23:59:57Z |
| format | Article |
| id | doaj.art-f4a159fa064f479e9f7d71ae6e2bc180 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-12-11T23:59:57Z |
| publishDate | 2016-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-f4a159fa064f479e9f7d71ae6e2bc1802022-12-22T00:45:15ZengMDPI AGAlgorithms1999-48932016-12-01948310.3390/a9040083a9040083Nonsmooth Levenberg-Marquardt Type Method for Solving a Class of Stochastic Linear Complementarity Problems with Finitely Many ElementsZhimin Liu0Shouqiang Du1Ruiying Wang2School of Mathematics and Statistics, Qingdao University, 308 Qingdao Ningxia Road, Qingdao 266071, ChinaSchool of Mathematics and Statistics, Qingdao University, 308 Qingdao Ningxia Road, Qingdao 266071, ChinaSchool of Mathematics and Statistics, Qingdao University, 308 Qingdao Ningxia Road, Qingdao 266071, ChinaOur purpose of this paper is to solve a class of stochastic linear complementarity problems (SLCP) with finitely many elements. Based on a new stochastic linear complementarity problem function, a new semi-smooth least squares reformulation of the stochastic linear complementarity problem is introduced. For solving the semi-smooth least squares reformulation, we propose a feasible nonsmooth Levenberg–Marquardt-type method. The global convergence properties of the nonsmooth Levenberg–Marquardt-type method are also presented. Finally, the related numerical results illustrate that the proposed method is efficient for the related refinery production problem and the large-scale stochastic linear complementarity problems.http://www.mdpi.com/1999-4893/9/4/83nonsmooth equationsstochastic linear complementarity problemsglobal convergenceLevenberg–Marquardt-type method |
| spellingShingle | Zhimin Liu Shouqiang Du Ruiying Wang Nonsmooth Levenberg-Marquardt Type Method for Solving a Class of Stochastic Linear Complementarity Problems with Finitely Many Elements Algorithms nonsmooth equations stochastic linear complementarity problems global convergence Levenberg–Marquardt-type method |
| title | Nonsmooth Levenberg-Marquardt Type Method for Solving a Class of Stochastic Linear Complementarity Problems with Finitely Many Elements |
| title_full | Nonsmooth Levenberg-Marquardt Type Method for Solving a Class of Stochastic Linear Complementarity Problems with Finitely Many Elements |
| title_fullStr | Nonsmooth Levenberg-Marquardt Type Method for Solving a Class of Stochastic Linear Complementarity Problems with Finitely Many Elements |
| title_full_unstemmed | Nonsmooth Levenberg-Marquardt Type Method for Solving a Class of Stochastic Linear Complementarity Problems with Finitely Many Elements |
| title_short | Nonsmooth Levenberg-Marquardt Type Method for Solving a Class of Stochastic Linear Complementarity Problems with Finitely Many Elements |
| title_sort | nonsmooth levenberg marquardt type method for solving a class of stochastic linear complementarity problems with finitely many elements |
| topic | nonsmooth equations stochastic linear complementarity problems global convergence Levenberg–Marquardt-type method |
| url | http://www.mdpi.com/1999-4893/9/4/83 |
| work_keys_str_mv | AT zhiminliu nonsmoothlevenbergmarquardttypemethodforsolvingaclassofstochasticlinearcomplementarityproblemswithfinitelymanyelements AT shouqiangdu nonsmoothlevenbergmarquardttypemethodforsolvingaclassofstochasticlinearcomplementarityproblemswithfinitelymanyelements AT ruiyingwang nonsmoothlevenbergmarquardttypemethodforsolvingaclassofstochasticlinearcomplementarityproblemswithfinitelymanyelements |