Fukuda, Mituhiro; Kojima, Masakazu; Shida, Masayuki Lagrangian dual interior-point methods for semidefinite programs. (English) Zbl 1035.90054 SIAM J. Optim. 12, No. 4, 1007-1031 (2002). Summary: This paper proposes a new predictor-corrector interior-point method for a class of semidefinite programs, which numerically traces the central trajectory in a space of Lagrange multipliers. The distinguishing features of the method are full use of the BFGS quasi-Newton method in the corrector procedure and an application of the conjugate gradient method with an effective preconditioning matrix induced from the BFGS quasi-Newton method in the predictor procedure. Some preliminary numerical results are reported. Cited in 5 Documents MSC: 90C22 Semidefinite programming 90C51 Interior-point methods 90C53 Methods of quasi-Newton type 65F10 Iterative numerical methods for linear systems 49N15 Duality theory (optimization) 49M29 Numerical methods involving duality Keywords:semidefinite program; linear program over convex cones; primal-dual interior-point method; predictor-corrector method; Lagrangian dual; BFGS quasi-Newton method; conjugate gradient method Software:SDPLR; PREQN; L-BFGS; SDPT3; CSDP; SDPA; COL; SeDuMi PDFBibTeX XMLCite \textit{M. Fukuda} et al., SIAM J. Optim. 12, No. 4, 1007--1031 (2002; Zbl 1035.90054) Full Text: DOI