ISSN:
1436-4646
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract For a given map f from the n-dimensional Euclidean space En into itself, we consider the complementary problem of finding a nonnegative vector x in En whose imagef(x) is also nonnegative and such that the two vectors are orthogonal. It is the unifying mathematical form for several problems arising in different fields such as mathematical programming, game theory and economics. In this paper a new algorithm is developed based on the “adjacent simplex technique ”, which was used by Garcia, Lemke and Lüthi for approximating an equilibrium point of a noncooperative n-person game. An “almost-complementary” path leads to a “complementary” simplex, which approximates a stationary point. Because most of the existence proofs for the nonlinear complementarity use the relationship between stationary points and complementarity, the algorithm gives constructive proofs for many existence theorems. If a better approximation is desired, the algorithm may be restarted from any point. The dimension of the simplices on the path is varying, which computationally should result in some savings.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01681351
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