An infeasible-interior-point predictor-corrector algorithm for the second-order cone program

A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming (SOCP) by using the Alizadeh—Haeberly—Overton (AHO) search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an ɛ-approximate solution of an SOCP in at most O√n ln (ɛ0/ɛ)) iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.