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

Abstract

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 Fukushima's merit function. However, we use the direction to reduce the distance function ( 1 2 )∥u − u∗∥ 2 G , 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.