INTERIOR-POINT TRAJECTORIES IN SEMIDEFINITE PROGRAMMING

In this paper we study interior point trajectories in semidefinite pro gramming (SDP) including the central path of an SDP. This work was ins pired by the seminal work of Megiddo on linear programming trajectorie s [Progress in Math. Programming: Interior-Point Algorithms and Relate d Methods, N. Megiddo, ed., Springer-Verlag, Berlin, 1989, pp. 131 - 1 58]. Under an assumption of primal and dual strict feasibility, we sho w that the primal and dual central paths exist and converge to the ana lytic centers of the optimal faces of, respectively, the primal and th e dual problems. We consider a class of trajectories that are similar to the central path but can be constructed to pass through any given i nterior feasible or infeasible point, and study their convergence. Fin ally, we study the derivatives of these trajectories and their converg ence.