Uniqueness of the Minimal l1-Norm Solution to the Monotone Linear Complementarity Problem
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-01-04
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
The linear complementarity problem (LCP) has wide applications in economic equilibrium, operations research, and so on, which attracted a lot of interest of experts.
Finding the sparsest solution to the LCP has real applications in the field of portfolio selection and bimatrix game.
Motivated by the approach developed in compressive sensing, we may try to solve an l1-minimization problem to obtain the sparsest solution to the LCP, where an important theoretical problem is to investigate uniqueness of the solution to the concerned l1-minimization problem.
In this paper, we investigate the problem of finding the minimal l1-norm solution to the monotone LCP and propose a sufficient and necessary condition for the uniqueness of the minimal l1-norm solution to the monotone LCP, which provides an important theoretical basis for finding the sparsest solution to the monotone LCP via solving the corresponding l1-minimization problem.
Furthermore, several examples are given to confirm our theoretical finding.
American Psychological Association (APA)
Zhang, Ting& Jiang, Xiaoqin. 2017. Uniqueness of the Minimal l1-Norm Solution to the Monotone Linear Complementarity Problem. Mathematical Problems in Engineering،Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1191681
Modern Language Association (MLA)
Zhang, Ting& Jiang, Xiaoqin. Uniqueness of the Minimal l1-Norm Solution to the Monotone Linear Complementarity Problem. Mathematical Problems in Engineering No. 2017 (2017), pp.1-8.
https://search.emarefa.net/detail/BIM-1191681
American Medical Association (AMA)
Zhang, Ting& Jiang, Xiaoqin. Uniqueness of the Minimal l1-Norm Solution to the Monotone Linear Complementarity Problem. Mathematical Problems in Engineering. 2017. Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1191681
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1191681