Condition for global convergence of a homotopy method for variational inequality problems on unbounded sets

Authors:
Qing Xu;Bo Yu;Guochen Feng;Chuangyin Dang
Affiliations:
School of Management, Fudan University, Shanghai, P.R. China;Department of Applied Mathematics, Dalian University of Technology, Liaoning, P.R. China;Institute of Mathematics, Jilin University, Jilin, P.R. China;Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong
Venue:
Optimization Methods & Software
Year:
2007

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Abstract

A condition for global convergence of a homotopy method for a variational inequality problem (VIP) on an unbounded set is introduced. The condition is derived from a concept of a solution at infinity to VIP. By an argument of the existence of a homotopy path, we show that VIP has a solution if it has no solution at infinity. It is proved that if any of several well-known conditions given in the literature holds, there is no solution at infinity. Furthermore, a globally convergent homotopy method is developed to compute a solution to VIP. Several numerical examples illustrate how to follow the homotopy path starting at an arbitrary point in the unbounded set.