INTERIOR POINT ALGORITHMS FOR SOME MONOTONE VARIATIONAL INEQUALITY PROBLEMS

In this paper, the authors present two interior point algorithms for some monotone variational inequality problems. They show that the first algorithm is globally linearly convergent and generates and e- solution in polynomial iterations. Here each iteration takes only one Newton step over a parameterized linear equation. Then the algorithm is modified so that it turns to solve the same equation but with the parameter set to zero after a certain number of iterations. The modified algorithm is proved to be globally linearly and locally quadratically convergent under some assumptions. (A)