A new full-Newton step feasible interior point method for convex quadratic programming

A Full-Newton Step Interior-Point Method for Weighted Quadratic Programming Based on the Algebraic Equivalent Transformation

“…= γ and Lemma 2, the fourth equality is due to (15), the third inequality results from the fact that ∥x 2 ∥ ≤ ∥x∥ 2 for x ∈ R n , and the last inequality is due to (12). By taking the square root of both sides of the above inequality, the proof is complete.…”

“…In this section, we present computational results in the MATLAB environment to compare the proposed algorithm and the algorithm presented in [15]. We used the value of the accuracy parameter ε = 10 −4 .…”

“…. , x n s n ] T denotes the coordinate-wise (Hadamard) product of the vectors x and s. We consider the same central path as introduced in [15]. Let an initial point (x 0 , y 0 , s 0 ) ∈ F 0 be given; we define…”

“…Based on the function ψ(z) = √ z in the AET technique, Zhang et al [14] defined a predictor-corrector interior-point algorithm for P * (κ)-WLCP. Very recently, Boudjellal and Benterki [15] extended the full-Newton step feasible IPM to solve CQP problems based on replacing the complementarity condition by a non-negative weight vector.…”

“…By choosing appropriate values for the parameters, we obtain an iteration bound for WCQP with the same complexity as the one obtained for this type of problem. The novelty of the proposed method lies in the use of AET to solve the convex QP, which the method presented in [15] is a special case of our method for ψ(z) = z.…”