ISSN:
1572-9338
Keywords:
Variational inequality problem
;
nonlinear complementarity problem
;
simplicial algorithm
;
triangulation
;
piecewise linear approximation
;
convergence condition
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Economics
Notes:
Abstract In this paper we propose a variable dimension simplicial algorithm for solving the variational inequality problem on the cross product of the nonnegative orthant ℝ + m of them-dimensional Euclidean space ℝ m and then-dimensional unit simplexS n of ℝ n+1. Starting from an arbitrary point (u, v) єℝ + m ×S n, the algorithm generates a piecewise linear path in ℝ + m ×S n. The path is traced by making alternately linear programming pivot operations and replacement steps in an appropriate simplicial subdivision of ℝ + m ×S n. 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 (n+1)2 m rays to leave the starting point whereas the existing algorithm hasn+m+1 rays. A convergence condition is presented and the accuracy estimation of an approximate solution generated is also given.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02073592
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