Volume 6 Number 2 pp. 375-390 Restricted-step Josephy-Newton method for general variational inequalities with polyhedral constraints Mend-Amar Majig and Masao Fukushima Abstract In this paper, we consider the problem of finding a solution of the general (i.e., not necessarily monotone) variational inequality problem (VIP). We propose a new practical version of globally convergent Josephy-Newton based method for VIP. By means of some additional bound constraint, the method ensures existence of solutions to subproblems, which is an essential property not enjoyed by the classical Josephy-Newton method. Under appropriate conditions, global and locally superlinear convergence properties of the proposed method are established. Furthermore, we develop an evolutionary algorithm for solving general VIPs with bounded polyhedral constraints, which can be used to solve the modified Josephy-Newton subproblems when the constraint set is polyhedral. Numerical results for some test problems are reported to show the practical effectiveness of the proposed methods. Key words Mathematices Subject Classification variational inequality, merit function, Josephy-Newton method, evolutionary algorithm 65K05, 68T20 ONLINE SUBSCRIPTION (Institutional Subscription Only) Reference Copyright© 2010 Yokohama Publishers Back