An Analytic Center Cutting Plane Method for Solving Semi-Infinite Variational Inequality Problems

Authors:
Shu-Cherng Fang;Soon-Yi Wu;Jie Sun
Affiliations:
Industrial Engineering and Operations Research, North Carolina State University, Raleigh, NC 27695-7906, USA;Department of Mathematics, National Cheng Kung University, Tainan, Taiwan 700, ROC/ (E-mail: soonyi@mail.ncku.edu.tw;Department of Decision Sciences and Singapore-MIT Alliance, National University of Singapore, Republic of Singapore
Venue:
Journal of Global Optimization
Year:
2004

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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).