A class of projection and contraction methods for asymmetric linear variational inequalities and their relations to Fukushimaʹs 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 directions of Fukushimaʹs merit function. However, we use the direction to reduce the distance function (1/2) u − u* 2G, where μ* is a solution point of the problem. Finally, we report some numerical results for spatial price equilibrium problems by using the presented methods.