(1) School of Management, Fudan University, Shanghai, 200433, P.R. China;(2) Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning, 116024, P.R. China;(3) Institute of Mathematics, Jilin University, Changchum, Jilin, 130012, P.R. China
Abstract:
In this paper, for solving the finite-dimensional variational inequality problem
where F is a mapping from X to Rn, X = is nonempty (not necessarily bounded) and is a convex Cr+1 mapping, a homotopy method is presented. Under various conditions, existence and convergence of a smooth homotopy path from almost any interior initial point in X to a solution of the variational inequality problem is proven. It leads to an implementable and globally convergent algorithm and gives a new and constructive proof of existence of solution.
mapping from X to Rn, X =
is nonempty (not necessarily bounded) and
is a convex Cr+1 mapping, a homotopy method is presented. Under various conditions, existence and convergence of a smooth homotopy path from almost any interior initial point in X to a solution of the variational inequality problem is proven. It leads to an implementable and globally convergent algorithm and gives a new and constructive proof of existence of solution.