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Solving variational inequalities defined on a domain with infinitely many linear constraints |
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| Authors: | Shu-Cherng Fang Soonyi Wu Ş. İlker Birbil |
| Affiliation: | (1) Department of Industrial Engineering and Operations Research Program, North Carolina State University, Raleigh, NC 26695-7906, USA;(2) Departments of Mathematical Sciences and Industrial Engineering Program, Tsinghua University, Beijing, 100084, China;(3) Institute of Applied Mathematics, National Cheng Kung University, Tainan, 700, Taiwan, ROC;(4) Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, 34956, Turkey;(5) National Center for Theoretical Sciences, Tainan, Taiwan |
| Abstract: | We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper assumptions, the convergence results for both methods are given. We also provide numerical examples to illustrate the proposed methods. The work of S. Wu was partially supported by the National Science Council, Taiwan, ROC (Grant No. 19731001). S.-C. Fang’s research has been supported by the US Army Research Office (Grant No. W911NF-04-D-0003) and National Science Foundation (Grant No. DMI-0553310). |
| Keywords: | Variational inequality problem Analytic center based cutting plane method Discretization method Semi-infinite programming |
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