Algorithms For Variational Inequality In Finite Dimensional Space

Extragradient projection methods is an important algorithm for solv-ing variational inequalities. This method mainly consists of two steps: the firststep is to use a linesearch, the second step is to establish searching direction. Inthe first part, we use a new linesearch and a combination of searching direction.Then we present a new extragradient projection methods by searching directionfor solving variational inequalities. The double projection algorithm can get alonger iteration step length. It mainly consists of two steps: the first step is toconstruct a hyperplane by linesearch, which separates strictly current iterate fromthe solutions of the variational inequalities problem, the second step is to projectthe current iterate onto the intersection of the feasible set and the hyperplane.In the second part, we present a new linesearch for double projection algorithmand construct a hyperplane by linesearch. It not only separate strictly currentiterate from the solutions, but also it is more close to the solution.