A feasible primal–dual interior point method for linear semidefinite programming

In this paper, we consider a feasible primal–dual interior point method for linear semidefinite programming problem (SDP)(SDP) based on Alizadeh–Haeberly–Overton (AHO) direction (Monteiro, 1997). Firstly, and by a new and simple technique, we establish the existence and uniqueness of optimal solution of the perturbed problem (SDP)μ(SDP)μ and its convergence to optimal solution of (SDP)(SDP). Next, we present new different alternatives to calculate the displacement step. After, we establish the convergence of the obtained algorithm and we show that its complexity is O(nln[ε−1(〈X0,S0〉)]). Finally, we present some numerical simulations which show the effectiveness of the algorithm developed in this work.