Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results
Primal-dual interior-point path-following methods for semidefiniteprogramming (SDP) are considered. Several variants are discussed,based on Newton's method applied to three equations: primal feasibility,dual feasibility, and some form of centering condition. The focusis on three such algorithms, called respectively the XZ, XZ+ZX andQ methods. For the XZ+ZX and Q algorithms, the Newton system iswell-defined and its Jacobian is nonsingular at the solution, under nondegeneracyassumptions....
Published in 1994.