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|Title:||An analytic center cutting plane method for solving semi-infinite variational inequality problems|
Cutting plane methods
|Source:||Fang, S.-C., Wu, S.-Y., Sun, J. (2004). An analytic center cutting plane method for solving semi-infinite variational inequality problems. Journal of Global Optimization 28 (2) : 141-152. ScholarBank@NUS Repository. https://doi.org/10.1023/B:JOGO.0000015308.49676.ea|
|Abstract:||We study a variational inequality problem VI(X, F) with X being defined by infinitely many inequality constraints and F being a pseudomonotone function. It is shown that such problem can be reduced to a problem of finding a feasible point in a convex set defined by infinitely many constraints. An analytic center based cutting plane algorithm is proposed for solving the reduced problem. Under proper assumptions, the proposed algorithm finds an ε-optimal solution in O* (n2/ρ2) iterations, where O* (·) represents the leading order, n is the dimension of X, ε is a user-specified tolerance, and ρ is the radius of a ball contained in the ε-solution set of VI(X, F).|
|Source Title:||Journal of Global Optimization|
|Appears in Collections:||Staff Publications|
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