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Lagrangian dual interior-point methods for semidefinite programs. (English) Zbl 1035.90054

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.

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
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