A class of projection and contraction methods for asymmetric linear variational inequalities and their relations to Fukushima's descent method

For solving asymmetric linear variational inequalities, we present a class of projection and contraction methods under the general G-norm. The search direction of our methods is just a convex combination of two descent direct ions of Fukushima's merit function. However, we use the direction to reduce the distance function (1/2)parallel to u--u*parallel to(G)(2), where u* is a solution point of the problem. Finally, we report some numerical results for spatial price equilibrium problems by using the presented methods. (C) 1999 Elsevier Science Ltd. All rights reserved.