Preprint A735/2013
An $\mathcal{O}(1/k^{3/2})$ 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 $\mathcal{O}(1/k^{3/2})$. The methods performs two types of iterations: under relaxed Hybrid  Proximal-Extragradient iterations and short-steps primal-dual interior point iterations.