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We consider in this paper an infeasible predictor–corrector primal–dual path following interior point algorithm using the Nesterov–Todd search direction to solve semi-definite linear complementarity problems. Global convergence and polynomial iteration complexity of the algorithm are established. Two sufficient conditions are also given for superlinear convergence of iterates generated by the algorithm. Preliminary numerical results are finally provided when the algorithm is used to solve semi-definite linear complementarity problems.

computational optimization and applications

Interior point method on semi-definite linear complementarity problems using the Nesterov–Todd (NT) search direction: polynomial complexity and local convergence