Preprint A744/2014
An O(1/k^{3/2}) Hybrid Proximal Extragradient Primal-Dual interior point method for non-linear monotone complementarity problems
Mauricio Romero Sicre | Benar Fux Svaiter

 We present a mixed Newton-type Hybrid Proximal Extragradient, primal-dual  interior point method for solving smooth monotone complementarity problems.   Dual variables for the non-negativity constraints are introduced. The ergodic complexity of the method is O(1/k^{3/2}). The methods performs two types of iterations: under relaxes Hybrid   Proximal-Extragradient iterations and short-steps primal-dual interior   point iterations.