An LQP-based descent method for structured monotone variational inequalities

This paper proposes a descent method to solve a class of structured monotone variational inequalities. The descent directions are constructed from the iterates generated by a prediction-correction method [B.S. He, Y. Xu, X.M. Yuan, A logarithmic-quadratic proximal prediction-correction method for structured monotone variational inequalities, Comput. Optim. Appl. 35 (2006) 19-46], which is based on the logarithmic-quadratic proximal method. In addition, the optimal step-sizes along these descent directions are identified to accelerate the convergence of the new method. Finally, some numerical results for solving traffic equilibrium problems are reported. (C) 2010 Elsevier B.V. All rights reserved.