A note on the local convergence of predictor-corrector interior-point algorithm for the semidefinite linear complementarity problem using the Alizadeh–Haeberly–Overton search direction

Abstract. This note points out an error in the local quadratic convergence proof of the predictor-corrector interior-point algorithm for solving the semidefinite linear complementarity problem based on the Alizadeh–Haeberly–Overton search direction presented in [M. Kojima, M. Shida, and S. Shin-doh, SIAM J. Optim., 9 (1999), pp. 444–465]. Their algorithm is slightly modified and the local quadratic convergence of the resulting method is established. Key words. semidefinite linear complementarity problem, semidefinite programming, interior-point algorithm, predictor-corrector algorithm, local quadratic convergenc