The (n+1)2 m-ray algorithm: A new simplicial algorithm for the variational inequality problem on

In this paper the authors propose a variable dimension simplicial algorithm for solving the variational inequality problem on the cross product of the nonnegative orthant of the m-dimensional Euclidean space and the n-dimensional unit simplex of . Starting from an arbitrary point , the algorithm generates a piecewise linear path in . The path is traced by making alternatively linear programming pivot operations and replacement steps in an appropriate simplicial subdivision of . The algorithm differs from the thus far known algorithm in the number of directions in which it may leave the starting point. More precisely, the algorithm has rays to leave the starting point whereas the existing algorithm has rays. A convergence condition is presented and the accuracy estimation of an approximate solution generated is also given.