JAMC J Appl Math Comput (2012) 38:535–549 DOI 10.1007/s12190-011-0495-y An alternating direction method for general variational inequalities Abdellah Bnouhachem · Muhammad Aslam Noor · Mohamed Khalfaoui · Sheng Zhaohan Received: 16 October 2010 / Published online: 14 June 2011 © Korean Society for Computational and Applied Mathematics 2011 Abstract In this paper, we present an alternating direction method for structured general variational inequalities. This method only needs functional values for given variables in the solution process and does not require the estimate of the co-coercive modulus. All the computing process are easily implemented and the global conver- gence is also presented under mild assumptions. Some preliminary computational results are given. Keywords General variational inequalities · Alternating direction methods · Monotone operators Mathematics Subject Classification (2000) 49J40 · 65N30 1 Introduction Let A ∈ R m×n and b ∈ R m , X ⊂ R n be a nonempty closed convex set and f and g be continuous mapping from R n into itself. In this paper, we focus on the following A. Bnouhachem ( ) · S. Zhaohan School of Management Science and Engineering, Nanjing University, Nanjing 210093, P.R. China e-mail: babedallah@yahoo.com A. Bnouhachem Ibn Zohr University, ENSA, BP 32/S, Agadir, Morocco M.A. Noor Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan M.A. Noor Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia M. Khalfaoui Ibn Zohr University, Présidence, BP 32/S, Agadir, Morocco